diff --git a/flake.lock b/flake.lock
index 8d6445d3..53b65eb4 100644
--- a/flake.lock
+++ b/flake.lock
@@ -10,11 +10,11 @@
         ]
       },
       "locked": {
-        "lastModified": 1683314474,
-        "narHash": "sha256-gfHYpOnVTfS+4fhScBhfkB/e5z+jPFCi8zSy+aEh+8s=",
+        "lastModified": 1683909802,
+        "narHash": "sha256-2CL8NYKLYwwy6n0RyldvH86ULgrSvfzHrgq2Qf0ZUkE=",
         "owner": "AztecProtocol",
         "repo": "barretenberg",
-        "rev": "ad615ee7dc931d3dbea041e47c96b9d8dccebf98",
+        "rev": "97c9bc72aebab850b4a647d6e6cc50085226eafb",
         "type": "github"
       },
       "original": {
diff --git a/src/barretenberg_structures.rs b/src/barretenberg_structures.rs
index ec2334a8..18af9d15 100644
--- a/src/barretenberg_structures.rs
+++ b/src/barretenberg_structures.rs
@@ -1,3 +1,4 @@
+use acvm::acir::circuit::opcodes::MemoryBlock;
 use acvm::acir::circuit::{Circuit, Opcode};
 use acvm::acir::native_types::Expression;
 use acvm::acir::BlackBoxFunc;
@@ -426,6 +427,7 @@ pub(crate) struct ConstraintSystem {
     schnorr_constraints: Vec<SchnorrConstraint>,
     ecdsa_secp256k1_constraints: Vec<EcdsaConstraint>,
     blake2s_constraints: Vec<Blake2sConstraint>,
+    block_constraints: Vec<BlockConstraint>,
     keccak_constraints: Vec<Keccak256Constraint>,
     pedersen_constraints: Vec<PedersenConstraint>,
     hash_to_field_constraints: Vec<HashToFieldConstraint>,
@@ -538,6 +540,11 @@ impl ConstraintSystem {
         self.constraints = constraints;
         self
     }
+
+    pub(crate) fn block_constraints(mut self, block_constraints: Vec<BlockConstraint>) -> Self {
+        self.block_constraints = block_constraints;
+        self
+    }
 }
 
 impl ConstraintSystem {
@@ -641,13 +648,91 @@ impl ConstraintSystem {
             buffer.extend(&constraint.to_bytes());
         }
 
+        // Serialize each Block constraint
+        let len = self.block_constraints.len() as u32;
+        buffer.extend_from_slice(&len.to_be_bytes());
+        for constraint in self.block_constraints.iter() {
+            buffer.extend(&constraint.to_bytes());
+        }
+
+        buffer
+    }
+}
+
+#[derive(Clone, Hash, Debug)]
+pub(crate) struct MemOpBarretenberg {
+    pub(crate) is_store: i8,
+    pub(crate) index: Constraint,
+    pub(crate) value: Constraint,
+}
+impl MemOpBarretenberg {
+    fn to_bytes(&self) -> Vec<u8> {
+        let mut buffer = Vec::new();
+
+        buffer.extend_from_slice(&self.is_store.to_be_bytes());
+        buffer.extend_from_slice(&self.index.to_bytes());
+        buffer.extend_from_slice(&self.value.to_bytes());
+
+        buffer
+    }
+}
+
+#[derive(Clone, Hash, Debug)]
+pub(crate) struct BlockConstraint {
+    pub(crate) init: Vec<Constraint>,
+    pub(crate) trace: Vec<MemOpBarretenberg>,
+    pub(crate) is_ram: i8,
+}
+
+impl BlockConstraint {
+    fn to_bytes(&self) -> Vec<u8> {
+        let mut buffer = Vec::new();
+
+        let len = self.init.len() as u32;
+        buffer.extend_from_slice(&len.to_be_bytes());
+        for value in self.init.iter() {
+            buffer.extend_from_slice(&value.to_bytes());
+        }
+
+        let len = self.trace.len() as u32;
+        buffer.extend_from_slice(&len.to_be_bytes());
+        for op in self.trace.iter() {
+            buffer.extend_from_slice(&op.to_bytes());
+        }
+        buffer.extend_from_slice(&self.is_ram.to_be_bytes());
+
         buffer
     }
+
+    fn from_memory_block(b: &MemoryBlock, is_ram_block: bool) -> BlockConstraint {
+        let mut init = Vec::new();
+        let mut trace = Vec::new();
+        let len = b.len as usize;
+        for op in b.trace.iter().take(len) {
+            assert_eq!(op.operation, Expression::one());
+            init.push(serialize_arithmetic_gates(&op.value));
+        }
+        for op in b.trace.iter().skip(len) {
+            let index = serialize_arithmetic_gates(&op.index);
+            let value = serialize_arithmetic_gates(&op.value);
+            let bb_op = MemOpBarretenberg {
+                is_store: op.operation.to_const().unwrap().to_u128() as i8,
+                index,
+                value,
+            };
+            trace.push(bb_op);
+        }
+        let is_ram = i8::from(is_ram_block);
+        BlockConstraint {
+            init,
+            trace,
+            is_ram,
+        }
+    }
 }
 
 impl TryFrom<&Circuit> for ConstraintSystem {
     type Error = Error;
-
     /// Converts an `IR` into the `StandardFormat` constraint system
     fn try_from(circuit: &Circuit) -> Result<Self, Self::Error> {
         // Create constraint system
@@ -656,6 +741,7 @@ impl TryFrom<&Circuit> for ConstraintSystem {
         let mut logic_constraints: Vec<LogicConstraint> = Vec::new();
         let mut sha256_constraints: Vec<Sha256Constraint> = Vec::new();
         let mut blake2s_constraints: Vec<Blake2sConstraint> = Vec::new();
+        let mut block_constraints: Vec<BlockConstraint> = Vec::new();
         let mut keccak_constraints: Vec<Keccak256Constraint> = Vec::new();
         let mut pedersen_constraints: Vec<PedersenConstraint> = Vec::new();
         let mut compute_merkle_root_constraints: Vec<ComputeMerkleRootConstraint> = Vec::new();
@@ -1044,8 +1130,14 @@ impl TryFrom<&Circuit> for ConstraintSystem {
                 Opcode::Directive(_) | Opcode::Oracle(_) => {
                     // Directives & Oracles are only needed by the pwg
                 }
-                Opcode::Block(_) | Opcode::RAM(_) | Opcode::ROM(_) => {
-                    // TODO: implement serialization to match BB's interface
+                Opcode::Block(_) => {
+                    // Block is managed by ACVM
+                }
+                Opcode::RAM(block) => {
+                    block_constraints.push(BlockConstraint::from_memory_block(block, true))
+                }
+                Opcode::ROM(block) => {
+                    block_constraints.push(BlockConstraint::from_memory_block(block, false))
                 }
             }
         }
@@ -1062,6 +1154,7 @@ impl TryFrom<&Circuit> for ConstraintSystem {
             schnorr_constraints,
             ecdsa_secp256k1_constraints,
             blake2s_constraints,
+            block_constraints,
             keccak_constraints,
             hash_to_field_constraints,
             constraints,
diff --git a/src/composer.rs b/src/composer.rs
index 990b7bf3..2fa724ad 100644
--- a/src/composer.rs
+++ b/src/composer.rs
@@ -398,8 +398,9 @@ mod test {
     use super::*;
     use crate::{
         barretenberg_structures::{
-            ComputeMerkleRootConstraint, Constraint, Keccak256Constraint, LogicConstraint,
-            PedersenConstraint, RangeConstraint, SchnorrConstraint,
+            BlockConstraint, ComputeMerkleRootConstraint, Constraint, Keccak256Constraint,
+            LogicConstraint, MemOpBarretenberg, PedersenConstraint, RangeConstraint,
+            SchnorrConstraint,
         },
         merkle::{MerkleTree, MessageHasher},
     };
@@ -769,6 +770,112 @@ mod test {
         test_composer_with_pk_vk(constraint_system, vec![case_1])
     }
 
+    #[test]
+    fn test_memory_constraints() -> Result<(), Error> {
+        let two_field = FieldElement::one() + FieldElement::one();
+        let one = Constraint {
+            a: 0,
+            b: 0,
+            c: 0,
+            qm: FieldElement::zero(),
+            ql: FieldElement::zero(),
+            qr: FieldElement::zero(),
+            qo: FieldElement::zero(),
+            qc: FieldElement::one(),
+        };
+
+        let two_x_constraint = Constraint {
+            a: 1,
+            b: 0,
+            c: 0,
+            qm: FieldElement::zero(),
+            ql: two_field,
+            qr: FieldElement::zero(),
+            qo: FieldElement::zero(),
+            qc: FieldElement::zero(),
+        };
+        let x_1_constraint = Constraint {
+            a: 1,
+            b: 0,
+            c: 0,
+            qm: FieldElement::zero(),
+            ql: FieldElement::one(),
+            qr: FieldElement::zero(),
+            qo: FieldElement::zero(),
+            qc: FieldElement::one(),
+        };
+
+        let y_constraint = Constraint {
+            a: 2,
+            b: 0,
+            c: 0,
+            qm: FieldElement::zero(),
+            ql: FieldElement::one(),
+            qr: FieldElement::zero(),
+            qo: FieldElement::zero(),
+            qc: FieldElement::zero(),
+        };
+        let z_constraint = Constraint {
+            a: 3,
+            b: 0,
+            c: 0,
+            qm: FieldElement::zero(),
+            ql: FieldElement::one(),
+            qr: FieldElement::zero(),
+            qo: FieldElement::zero(),
+            qc: FieldElement::zero(),
+        };
+        let op1 = MemOpBarretenberg {
+            index: two_x_constraint,
+            value: y_constraint,
+            is_store: 0,
+        };
+        let op2 = MemOpBarretenberg {
+            index: x_1_constraint.clone(),
+            value: z_constraint,
+            is_store: 0,
+        };
+        let block_constraint = BlockConstraint {
+            init: vec![one, x_1_constraint],
+            trace: vec![op1, op2],
+            is_ram: 0,
+        };
+
+        let result_constraint = Constraint {
+            a: 2,
+            b: 3,
+            c: 0,
+            qm: FieldElement::zero(),
+            ql: FieldElement::one(),
+            qr: FieldElement::one(),
+            qo: FieldElement::zero(),
+            qc: -(two_field),
+        };
+        let constraint_system = ConstraintSystem::new()
+            .var_num(4)
+            .block_constraints(vec![block_constraint])
+            .constraints(vec![result_constraint]);
+
+        let scalar_0 = FieldElement::zero();
+        let scalar_1 = FieldElement::one();
+        let witness_values = vec![scalar_0, scalar_1, scalar_1];
+
+        let case_1 = WitnessResult {
+            witness: witness_values.into(),
+            public_inputs: Assignments::default(),
+            result: true,
+        };
+
+        let bad_values = vec![scalar_0, scalar_1, scalar_1 + scalar_1];
+        let case_2 = WitnessResult {
+            witness: bad_values.into(),
+            public_inputs: Assignments::default(),
+            result: false,
+        };
+
+        test_composer_with_pk_vk(constraint_system, vec![case_1, case_2])
+    }
+
     #[test]
     fn test_compute_merkle_root_constraint() -> Result<(), Error> {
         use tempfile::tempdir;