diff --git a/.github/workflows/Lint.yml b/.github/workflows/Lint.yml
index 9f7e0655..d0ec5b81 100644
--- a/.github/workflows/Lint.yml
+++ b/.github/workflows/Lint.yml
@@ -6,7 +6,7 @@ jobs:
       fail-fast: false
       matrix:
         ruby: [2.6]
-        os: [ubuntu-16.04]
+        os: [ubuntu-18.04]
 
     name: Lint
     runs-on: ${{ matrix.os }}
diff --git a/.github/workflows/Specs.yml b/.github/workflows/Specs.yml
index f6c94dab..b5fde213 100644
--- a/.github/workflows/Specs.yml
+++ b/.github/workflows/Specs.yml
@@ -6,7 +6,7 @@ jobs:
       fail-fast: false
       matrix:
         ruby: ['2.1.9', '2.2', '2.3', '2.4', '2.5', '2.6', '2.7', '3.0']
-        os: [ubuntu-16.04]
+        os: [ubuntu-18.04]
         include:
           - os: macos-10.15
             ruby: system
diff --git a/CHANGELOG.md b/CHANGELOG.md
index a5c7b9d6..2f8e743e 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -4,6 +4,10 @@
 
 ##### Enhancements
 
+* Bump Xcode version to match Xcode 13  
+  [Eric Firestone](https://github.com/efirestone)
+  [#857](https://github.com/CocoaPods/Xcodeproj/pull/857)
+
 * Bump Xcode version constants for Xcode 12.5.  
   [Dimitris Koutsogiorgas](https://github.com/dnkoutso)
   [#856](https://github.com/CocoaPods/Xcodeproj/pull/856)
diff --git a/lib/xcodeproj/constants.rb b/lib/xcodeproj/constants.rb
index 2339acbc..81904d3d 100644
--- a/lib/xcodeproj/constants.rb
+++ b/lib/xcodeproj/constants.rb
@@ -36,11 +36,11 @@ module Constants
 
     # @return [String] The last known Xcode version to Xcodeproj.
     #
-    LAST_UPGRADE_CHECK = '1250'
+    LAST_UPGRADE_CHECK = '1300'
 
     # @return [String] The last known Xcode version to Xcodeproj.
     #
-    LAST_SWIFT_UPGRADE_CHECK = '1250'
+    LAST_SWIFT_UPGRADE_CHECK = '1300'
 
     # @return [String] The version of `.xcscheme` files supported by Xcodeproj
     #
diff --git a/spec/fixtures/Sample Project/Cocoa Application.xcodeproj/xcshareddata/xcschemes/iOS application and static library.xcscheme b/spec/fixtures/Sample Project/Cocoa Application.xcodeproj/xcshareddata/xcschemes/iOS application and static library.xcscheme
index a33abd75..0cebac12 100644
--- a/spec/fixtures/Sample Project/Cocoa Application.xcodeproj/xcshareddata/xcschemes/iOS application and static library.xcscheme	
+++ b/spec/fixtures/Sample Project/Cocoa Application.xcodeproj/xcshareddata/xcschemes/iOS application and static library.xcscheme	
@@ -1,6 +1,6 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <Scheme
-   LastUpgradeVersion = "1250"
+   LastUpgradeVersion = "1300"
    version = "1.3">
    <BuildAction
       parallelizeBuildables = "YES"
diff --git a/spec/fixtures/Sample Project/Cocoa Application.xcodeproj/xcshareddata/xcschemes/iOS application.xcscheme b/spec/fixtures/Sample Project/Cocoa Application.xcodeproj/xcshareddata/xcschemes/iOS application.xcscheme
index cc987c57..4f6a37f0 100644
--- a/spec/fixtures/Sample Project/Cocoa Application.xcodeproj/xcshareddata/xcschemes/iOS application.xcscheme	
+++ b/spec/fixtures/Sample Project/Cocoa Application.xcodeproj/xcshareddata/xcschemes/iOS application.xcscheme	
@@ -1,6 +1,6 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <Scheme
-   LastUpgradeVersion = "1250"
+   LastUpgradeVersion = "1300"
    version = "1.3">
    <BuildAction
       parallelizeBuildables = "YES"
diff --git a/spec/fixtures/Sample Project/Cocoa Application.xcodeproj/xcshareddata/xcschemes/iOS applicationTests Set Build Target For Running.xcscheme b/spec/fixtures/Sample Project/Cocoa Application.xcodeproj/xcshareddata/xcschemes/iOS applicationTests Set Build Target For Running.xcscheme
index 9aee486b..b79ac7d4 100644
--- a/spec/fixtures/Sample Project/Cocoa Application.xcodeproj/xcshareddata/xcschemes/iOS applicationTests Set Build Target For Running.xcscheme	
+++ b/spec/fixtures/Sample Project/Cocoa Application.xcodeproj/xcshareddata/xcschemes/iOS applicationTests Set Build Target For Running.xcscheme	
@@ -1,6 +1,6 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <Scheme
-   LastUpgradeVersion = "1250"
+   LastUpgradeVersion = "1300"
    version = "1.3">
    <BuildAction
       parallelizeBuildables = "YES"
diff --git a/spec/fixtures/Sample Project/Cocoa Application.xcodeproj/xcshareddata/xcschemes/iOS applicationTests.xcscheme b/spec/fixtures/Sample Project/Cocoa Application.xcodeproj/xcshareddata/xcschemes/iOS applicationTests.xcscheme
index 7454aba0..53e7abcf 100644
--- a/spec/fixtures/Sample Project/Cocoa Application.xcodeproj/xcshareddata/xcschemes/iOS applicationTests.xcscheme	
+++ b/spec/fixtures/Sample Project/Cocoa Application.xcodeproj/xcshareddata/xcschemes/iOS applicationTests.xcscheme	
@@ -1,6 +1,6 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <Scheme
-   LastUpgradeVersion = "1250"
+   LastUpgradeVersion = "1300"
    version = "1.3">
    <BuildAction
       parallelizeBuildables = "YES"
diff --git a/spec/scheme_spec.rb b/spec/scheme_spec.rb
index 4457f1dd..7bb68986 100644
--- a/spec/scheme_spec.rb
+++ b/spec/scheme_spec.rb
@@ -230,7 +230,7 @@ module ProjectSpecs
         expected = <<-XML.gsub(/^ {8}/, '')
         <?xml version="1.0" encoding="UTF-8"?>
         <Scheme
-           LastUpgradeVersion = "1250"
+           LastUpgradeVersion = "1300"
            version = "1.3">
            <BuildAction
               parallelizeBuildables = "YES"