diff --git a/botorch/test_functions/__init__.py b/botorch/test_functions/__init__.py
index 612d8d946d..136a3e0854 100644
--- a/botorch/test_functions/__init__.py
+++ b/botorch/test_functions/__init__.py
@@ -54,13 +54,17 @@
     Levy,
     Michalewicz,
     Powell,
+    PressureVessel,
     Rastrigin,
     Rosenbrock,
     Shekel,
     SixHumpCamel,
+    SpeedReducer,
     StyblinskiTang,
     SyntheticTestFunction,
+    TensionCompressionString,
     ThreeHumpCamel,
+    WeldedBeamSO,
 )
 
 
@@ -99,17 +103,21 @@
     "OSY",
     "Penicillin",
     "Powell",
+    "PressureVessel",
     "Rastrigin",
     "Rosenbrock",
     "Shekel",
     "SixHumpCamel",
+    "SpeedReducer",
     "SRN",
     "StyblinskiTang",
     "SyntheticTestFunction",
+    "TensionCompressionString",
     "ThreeHumpCamel",
     "ToyRobust",
     "VehicleSafety",
     "WeldedBeam",
+    "WeldedBeamSO",
     "ZDT1",
     "ZDT2",
     "ZDT3",
diff --git a/botorch/test_functions/multi_objective.py b/botorch/test_functions/multi_objective.py
index a46ea5373a..e9255fd76e 100644
--- a/botorch/test_functions/multi_objective.py
+++ b/botorch/test_functions/multi_objective.py
@@ -1444,7 +1444,10 @@ def evaluate_slack_true(self, X: Tensor) -> Tensor:
 
 class WeldedBeam(MultiObjectiveTestProblem, ConstrainedBaseTestProblem):
     r"""
-    The Welded Beam test problem.
+    The Welded Beam multi-objective test problem. Similar to `WeldedBeamSO` in
+    `botorch.test_function.synthetic`, but with an additional output, somewhat
+    modified constraints, and a different domain.
+
     Implementation from
     https://github.com/msu-coinlab/pymoo/blob/master/pymoo/problems/multi/welded_beam.py
     Note that this implementation assumes minimization, so please choose negate=True.
@@ -1462,35 +1465,44 @@ class WeldedBeam(MultiObjectiveTestProblem, ConstrainedBaseTestProblem):
     _ref_point = [40, 0.015]
 
     def evaluate_true(self, X: Tensor) -> Tensor:
-        f1 = 1.10471 * X[..., 0] ** 2 * X[..., 1] + 0.04811 * X[..., 2] * X[..., 3] * (
-            14.0 + X[..., 1]
-        )
-        f2 = 2.1952 / (X[..., 3] * X[..., 2] ** 3)
+        # We could do the following, but the constraints are using somewhat
+        # different numbers (see below).
+        # f1 = WeldedBeam.evaluate_true(self, X)
+        x1, x2, x3, x4 = X.unbind(-1)
+        f1 = 1.10471 * (x1**2) * x2 + 0.04811 * x3 * x4 * (14.0 + x2)
+        f2 = 2.1952 / (x4 * x3**3)
         return torch.stack([f1, f2], dim=-1)
 
     def evaluate_slack_true(self, X: Tensor) -> Tensor:
-        P = 6000
-        L = 14
-        t_max = 13600
-        s_max = 30000
-
-        R = torch.sqrt(0.25 * (X[..., 1] ** 2 + (X[..., 0] + X[..., 2]) ** 2))
-        M = P * (L + X[..., 1] / 2)
-        J = (
-            2
-            * math.sqrt(0.5)
-            * X[..., 0]
-            * X[..., 1]
-            * (X[..., 1] ** 2 / 12 + 0.25 * (X[..., 0] + X[..., 2]) ** 2)
-        )
-        t1 = P / (math.sqrt(2) * X[..., 0] * X[..., 1])
+        x1, x2, x3, x4 = X.unbind(-1)
+        P = 6000.0
+        L = 14.0
+        t_max = 13600.0
+        s_max = 30000.0
+
+        # Ideally, we could just do the following, but the numbers in the
+        # single-outcome WeldedBeam are different (see below)
+        # g1_, g2_, g3_, _, _, g6_ = WeldedBeam.evaluate_slack_true(self, X)
+        # g1 = g1_ / t_max
+        # g2 = g2_ / s_max
+        # g3 = 1 / (5 - 0.125) * g3_
+        # g4 = 1 / P * g6_
+
+        R = torch.sqrt(0.25 * (x2**2 + (x1 + x3) ** 2))
+        M = P * (L + x2 / 2)
+        # This `J` is different than the one in [CoelloCoello2002constraint]_
+        # by a factor of 2 (sqrt(2) instead of sqrt(0.5))
+        J = 2 * math.sqrt(0.5) * x1 * x2 * (x2**2 / 12 + 0.25 * (x1 + x3) ** 2)
+        t1 = P / (math.sqrt(2) * x1 * x2)
         t2 = M * R / J
-        t = torch.sqrt(t1**2 + t2**2 + t1 * t2 * X[..., 1] / R)
-        s = 6 * P * L / (X[..., 3] * X[..., 2] ** 2)
-        P_c = 64746.022 * (1 - 0.0282346 * X[..., 2]) * X[..., 2] * X[..., 3] ** 3
-
-        g1 = (1 / t_max) * (t - t_max)
-        g2 = (1 / s_max) * (s - s_max)
-        g3 = (1 / (5 - 0.125)) * (X[..., 0] - X[..., 3])
-        g4 = (1 / P) * (P - P_c)
-        return -torch.stack([g1, g2, g3, g4], dim=-1)
+        t = torch.sqrt(t1**2 + t1 * t2 * x2 / R + t2**2)
+        s = 6 * P * L / (x4 * x3**2)
+        # These numbers are also different from [CoelloCoello2002constraint]_
+        P_c = 64746.022 * (1 - 0.0282346 * x3) * x3 * x4**3
+
+        g1 = (t - t_max) / t_max
+        g2 = (s - s_max) / s_max
+        g3 = 1 / (5 - 0.125) * (x1 - x4)
+        g4 = (P - P_c) / P
+
+        return torch.stack([g1, g2, g3, g4], dim=-1)
diff --git a/botorch/test_functions/synthetic.py b/botorch/test_functions/synthetic.py
index f44cc1b5df..1e710fd06d 100644
--- a/botorch/test_functions/synthetic.py
+++ b/botorch/test_functions/synthetic.py
@@ -6,7 +6,32 @@
 
 r"""
 Synthetic functions for optimization benchmarks.
-Reference: https://www.sfu.ca/~ssurjano/optimization.html
+
+Most test functions (if not indicated otherwise) are taken from
+[Bingham2013virtual]_.
+
+
+References:
+
+.. [Bingham2013virtual]
+    D. Bingham, S. Surjanovic. Virtual Library of Simulation Experiments.
+    https://www.sfu.ca/~ssurjano/optimization.html
+
+.. [CoelloCoello2002constraint]
+    C. A. Coello Coello and E. Mezura Montes. Constraint-handling in genetic
+    algorithms through the use of dominance-based tournament selection.
+    Advanced Engineering Informatics, 16(3):193–203, 2002.
+
+.. [Hedar2006derivfree]
+    A.-R. Hedar and M. Fukushima. Derivative-free filter simulated annealing
+    method for constrained continuous global optimization. Journal of Global
+    Optimization, 35(4):521–549, 2006.
+
+.. [Lemonge2010constrained]
+    A. C. C. Lemonge, H. J. C. Barbosa, C. C. H. Borges, and F. B. dos Santos
+    Silva. Constrained optimization problems in mechanical engineering design
+    using a real-coded steady-state genetic algorithm. Mecánica Computacional,
+    XXIX:9287–9303, 2010.
 """
 
 from __future__ import annotations
@@ -15,7 +40,8 @@
 from typing import List, Optional, Tuple
 
 import torch
-from botorch.test_functions.base import BaseTestProblem
+from botorch.test_functions.base import BaseTestProblem, ConstrainedBaseTestProblem
+from botorch.test_functions.utils import round_nearest
 from torch import Tensor
 
 
@@ -761,3 +787,182 @@ class ThreeHumpCamel(SyntheticTestFunction):
     def evaluate_true(self, X: Tensor) -> Tensor:
         x1, x2 = X[..., 0], X[..., 1]
         return 2.0 * x1**2 - 1.05 * x1**4 + x1**6 / 6.0 + x1 * x2 + x2**2
+
+
+#  ------------ Constrained synthetic test functions ----------- #
+
+
+class PressureVessel(SyntheticTestFunction, ConstrainedBaseTestProblem):
+    r"""Pressure vessel design problem with constraints.
+
+    The four-dimensional pressure vessel design problem with four black-box
+    constraints from [CoelloCoello2002constraint]_.
+    """
+
+    dim = 4
+    num_constraints = 4
+    _bounds = [(0.0, 10.0), (0.0, 10.0), (10.0, 50.0), (150.0, 200.0)]
+
+    def evaluate_true(self, X: Tensor) -> Tensor:
+        x1, x2, x3, x4 = X.unbind(-1)
+        x1 = round_nearest(x1, increment=0.0625, bounds=self._bounds[0])
+        x2 = round_nearest(x2, increment=0.0625, bounds=self._bounds[1])
+        return (
+            0.6224 * x1 * x3 * x4
+            + 1.7781 * x2 * (x3**2)
+            + 3.1661 * (x1**2) * x4
+            + 19.84 * (x1**2) * x3
+        )
+
+    def evaluate_slack_true(self, X: Tensor) -> Tensor:
+        x1, x2, x3, x4 = X.unbind(-1)
+        return -torch.stack(
+            [
+                -x1 + 0.0193 * x3,
+                -x2 + 0.00954 * x3,
+                -math.pi * (x3**2) * x4 - (4 / 3) * math.pi * (x3**3) + 1296000.0,
+                x4 - 240.0,
+            ],
+            dim=-1,
+        )
+
+
+class WeldedBeamSO(SyntheticTestFunction, ConstrainedBaseTestProblem):
+    r"""Welded beam design problem with constraints (single-outcome).
+
+    The four-dimensional welded beam design proble problem with six
+    black-box constraints from [CoelloCoello2002constraint]_.
+
+    For a (somewhat modified) multi-objective version, see
+    `botorch.test_functions.multi_objective.WeldedBeam`.
+    """
+
+    dim = 4
+    num_constraints = 6
+    _bounds = [(0.125, 10.0), (0.1, 10.0), (0.1, 10.0), (0.1, 10.0)]
+
+    def evaluate_true(self, X: Tensor) -> Tensor:
+        x1, x2, x3, x4 = X.unbind(-1)
+        return 1.10471 * (x1**2) * x2 + 0.04811 * x3 * x4 * (14.0 + x2)
+
+    def evaluate_slack_true(self, X: Tensor) -> Tensor:
+        x1, x2, x3, x4 = X.unbind(-1)
+        P = 6000.0
+        L = 14.0
+        E = 30e6
+        G = 12e6
+        t_max = 13600.0
+        s_max = 30000.0
+        d_max = 0.25
+
+        M = P * (L + x2 / 2)
+        R = torch.sqrt(0.25 * (x2**2 + (x1 + x3) ** 2))
+        J = 2 * math.sqrt(2) * x1 * x2 * (x2**2 / 12 + 0.25 * (x1 + x3) ** 2)
+        P_c = (
+            4.013
+            * E
+            * x3
+            * (x4**3)
+            * 6
+            / (L**2)
+            * (1 - 0.25 * x3 * math.sqrt(E / G) / L)
+        )
+        t1 = P / (math.sqrt(2) * x1 * x2)
+        t2 = M * R / J
+        t = torch.sqrt(t1**2 + t1 * t2 * x2 / R + t2**2)
+        s = 6 * P * L / (x4 * x3**2)
+        d = 4 * P * L**3 / (E * x3**3 * x4)
+
+        g1 = t - t_max
+        g2 = s - s_max
+        g3 = x1 - x4
+        g4 = 0.10471 * x1**2 + 0.04811 * x3 * x4 * (14.0 + x2) - 5.0
+        g5 = d - d_max
+        g6 = P - P_c
+
+        return -torch.stack([g1, g2, g3, g4, g5, g6], dim=-1)
+
+
+class TensionCompressionString(SyntheticTestFunction, ConstrainedBaseTestProblem):
+    r"""Tension compression string optimization problem with constraints.
+
+    The three-dimensional tension compression string optimization problem with
+    four black-box constraints from [Hedar2006derivfree]_.
+    """
+
+    dim = 3
+    num_constraints = 4
+    _bounds = [(0.01, 1.0), (0.01, 1.0), (0.01, 20.0)]
+
+    def evaluate_true(self, X: Tensor) -> Tensor:
+        x1, x2, x3 = X.unbind(-1)
+        return (x1**2) * x2 * (x3 + 2)
+
+    def evaluate_slack_true(self, X: Tensor) -> Tensor:
+        x1, x2, x3 = X.unbind(-1)
+        constraints = torch.stack(
+            [
+                1 - (x2**3) * x3 / (71785 * (x1**4)),
+                (4 * (x2**2) - x1 * x2) / (12566 * (x1**3) * (x2 - x1))
+                + 1 / (5108 * (x1**2))
+                - 1,
+                1 - 140.45 * x1 / (x3 * (x2**2)),
+                (x1 + x2) / 1.5 - 1,
+            ],
+            dim=-1,
+        )
+        return -constraints.clamp_max(100)
+
+
+class SpeedReducer(SyntheticTestFunction, ConstrainedBaseTestProblem):
+    r"""Speed Reducer design problem with constraints.
+
+    The seven-dimensional speed reducer design problem with eleven black-box
+    constraints from [Lemonge2010constrained]_.
+    """
+
+    dim = 7
+    num_constraints = 11
+    _bounds = [
+        (2.6, 3.6),
+        (0.7, 0.8),
+        (17.0, 28.0),
+        (7.3, 8.3),
+        (7.8, 8.3),
+        (2.9, 3.9),
+        (5.0, 5.5),
+    ]
+
+    def evaluate_true(self, X: Tensor) -> Tensor:
+        x1, x2, x3, x4, x5, x6, x7 = X.unbind(-1)
+        return (
+            0.7854 * x1 * (x2**2) * (3.3333 * (x3**2) + 14.9334 * x3 - 43.0934)
+            + -1.508 * x1 * (x6**2 + x7**2)
+            + 7.4777 * (x6**3 + x7**3)
+            + 0.7854 * (x4 * (x6**2) + x5 * (x7**2))
+        )
+
+    def evaluate_slack_true(self, X: Tensor) -> Tensor:
+        x1, x2, x3, x4, x5, x6, x7 = X.unbind(-1)
+        return -torch.stack(
+            [
+                27.0 * (1 / x1) * (1 / (x2**2)) * (1 / x3) - 1,
+                397.5 * (1 / x1) * (1 / (x2**2)) * (1 / (x3**2)) - 1,
+                1.93 * (1 / x2) * (1 / x3) * (x4**3) * (1 / (x6**4)) - 1,
+                1.93 * (1 / x2) * (1 / x3) * (x5**3) * (1 / (x7**4)) - 1,
+                1
+                / (0.1 * (x6**3))
+                * torch.sqrt((745 * x4 / (x2 * x3)) ** 2 + 16.9 * 1e6)
+                - 1100,
+                1
+                / (0.1 * (x7**3))
+                * torch.sqrt((745 * x5 / (x2 * x3)) ** 2 + 157.5 * 1e6)
+                - 850,
+                x2 * x3 - 40,
+                5 - x1 / x2,
+                x1 / x2 - 12,
+                (1.5 * x6 + 1.9) / x4 - 1,
+                (1.1 * x7 + 1.9) / x5 - 1,
+            ],
+            dim=-1,
+        )
diff --git a/botorch/test_functions/utils.py b/botorch/test_functions/utils.py
new file mode 100644
index 0000000000..969524822d
--- /dev/null
+++ b/botorch/test_functions/utils.py
@@ -0,0 +1,36 @@
+#!/usr/bin/env python3
+# Copyright (c) Meta Platforms, Inc. and affiliates.
+#
+# This source code is licensed under the MIT license found in the
+# LICENSE file in the root directory of this source tree.
+
+
+from __future__ import annotations
+
+from typing import Optional, Tuple
+
+import torch
+
+from torch import Tensor
+
+
+def round_nearest(
+    X: Tensor, increment: float, bounds: Optional[Tuple[float, float]]
+) -> Tensor:
+    r"""Rounds the input tensor to the nearest multiple of `increment`.
+
+    Args:
+        X: The input to be rounded.
+        increment: The increment to round to.
+        bounds: An optional tuple of two floats representing the lower and upper
+            bounds on `X`. If provided, this will round to the nearest multiple
+            of `increment` that lies within the bounds.
+
+    Returns:
+        The rounded input.
+    """
+    X_round = torch.round(X / increment) * increment
+    if bounds is not None:
+        X_round = torch.where(X_round < bounds[0], X_round + increment, X_round)
+        X_round = torch.where(X_round > bounds[1], X_round - increment, X_round)
+    return X_round
diff --git a/sphinx/source/test_functions.rst b/sphinx/source/test_functions.rst
index cf9e324b37..bfde346766 100644
--- a/sphinx/source/test_functions.rst
+++ b/sphinx/source/test_functions.rst
@@ -35,3 +35,8 @@ Sensitivity Analysis Test Functions
 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 .. automodule:: botorch.test_functions.sensitivity_analysis
     :members:
+
+Utilities For Test Functions
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+.. automodule:: botorch.test_functions.utils
+    :members:
diff --git a/test/test_functions/test_synthetic.py b/test/test_functions/test_synthetic.py
index 9c37979970..4e8198f6cf 100644
--- a/test/test_functions/test_synthetic.py
+++ b/test/test_functions/test_synthetic.py
@@ -21,17 +21,22 @@
     Levy,
     Michalewicz,
     Powell,
+    PressureVessel,
     Rastrigin,
     Rosenbrock,
     Shekel,
     SixHumpCamel,
+    SpeedReducer,
     StyblinskiTang,
     SyntheticTestFunction,
+    TensionCompressionString,
     ThreeHumpCamel,
+    WeldedBeamSO,
 )
 from botorch.utils.testing import (
     BaseTestProblemTestCaseMixIn,
     BotorchTestCase,
+    ConstrainedTestProblemTestCaseMixin,
     SyntheticTestFunctionTestCaseMixin,
 )
 from torch import Tensor
@@ -308,3 +313,42 @@ class TestThreeHumpCamel(
         ThreeHumpCamel(negate=True),
         ThreeHumpCamel(noise_std=0.1),
     ]
+
+
+# ------------------ Constrained synthetic test problems ------------------ #
+
+
+class TestPressureVessel(
+    BotorchTestCase,
+    BaseTestProblemTestCaseMixIn,
+    ConstrainedTestProblemTestCaseMixin,
+):
+
+    functions = [PressureVessel()]
+
+
+class TestSpeedReducer(
+    BotorchTestCase,
+    BaseTestProblemTestCaseMixIn,
+    ConstrainedTestProblemTestCaseMixin,
+):
+
+    functions = [SpeedReducer()]
+
+
+class TestTensionCompressionString(
+    BotorchTestCase,
+    BaseTestProblemTestCaseMixIn,
+    ConstrainedTestProblemTestCaseMixin,
+):
+
+    functions = [TensionCompressionString()]
+
+
+class TestWeldedBeamSO(
+    BotorchTestCase,
+    BaseTestProblemTestCaseMixIn,
+    ConstrainedTestProblemTestCaseMixin,
+):
+
+    functions = [WeldedBeamSO()]