diff --git a/llvm/include/llvm/Analysis/InstructionSimplify.h b/llvm/include/llvm/Analysis/InstructionSimplify.h
--- a/llvm/include/llvm/Analysis/InstructionSimplify.h
+++ b/llvm/include/llvm/Analysis/InstructionSimplify.h
@@ -259,6 +259,10 @@
 /// Given a callsite, fold the result or return null.
 Value *SimplifyCall(CallBase *Call, const SimplifyQuery &Q);
 
+/// Given an operand for a Freeze, see if we can fold the result.
+/// If not, this returns null.
+Value *SimplifyFreezeInst(Value *Op, const SimplifyQuery &Q);
+
 /// See if we can compute a simplified version of this instruction. If not,
 /// return null.
 Value *SimplifyInstruction(Instruction *I, const SimplifyQuery &Q,
diff --git a/llvm/include/llvm/Analysis/ValueTracking.h b/llvm/include/llvm/Analysis/ValueTracking.h
--- a/llvm/include/llvm/Analysis/ValueTracking.h
+++ b/llvm/include/llvm/Analysis/ValueTracking.h
@@ -561,6 +561,10 @@
   /// the parent of I.
   bool programUndefinedIfFullPoison(const Instruction *PoisonI);
 
+  /// Return true if this function can prove that V is never undef value
+  /// or poison value.
+  bool isGuaranteedNotToBeUndefOrPoison(const Value *V);
+
   /// Specific patterns of select instructions we can match.
   enum SelectPatternFlavor {
     SPF_UNKNOWN = 0,
diff --git a/llvm/lib/Analysis/InstructionSimplify.cpp b/llvm/lib/Analysis/InstructionSimplify.cpp
--- a/llvm/lib/Analysis/InstructionSimplify.cpp
+++ b/llvm/lib/Analysis/InstructionSimplify.cpp
@@ -5241,6 +5241,19 @@
   return ConstantFoldCall(Call, F, ConstantArgs, Q.TLI);
 }
 
+/// Given operands for a Freeze, see if we can fold the result.
+static Value *SimplifyFreezeInst(Value *Op0) {
+  // Use a utility function defined in ValueTracking.
+  if (llvm::isGuaranteedNotToBeUndefOrPoison(Op0))
+    return Op0;
+  // We have room for improvement.
+  return nullptr;
+}
+
+Value *llvm::SimplifyFreezeInst(Value *Op0, const SimplifyQuery &Q) {
+  return ::SimplifyFreezeInst(Op0);
+}
+
 /// See if we can compute a simplified version of this instruction.
 /// If not, this returns null.
 
@@ -5383,6 +5396,9 @@
     Result = SimplifyCall(cast<CallInst>(I), Q);
     break;
   }
+  case Instruction::Freeze:
+    Result = SimplifyFreezeInst(I->getOperand(0), Q);
+    break;
 #define HANDLE_CAST_INST(num, opc, clas) case Instruction::opc:
 #include "llvm/IR/Instruction.def"
 #undef HANDLE_CAST_INST
diff --git a/llvm/lib/Analysis/ValueTracking.cpp b/llvm/lib/Analysis/ValueTracking.cpp
--- a/llvm/lib/Analysis/ValueTracking.cpp
+++ b/llvm/lib/Analysis/ValueTracking.cpp
@@ -4221,6 +4221,20 @@
   return llvm::any_of(GuardingBranches, AllUsesGuardedByBranch);
 }
 
+bool llvm::isGuaranteedNotToBeUndefOrPoison(const Value *V) {
+  // If the value is a freeze instruction, then it can never
+  // be undef or poison.
+  if (isa<FreezeInst>(V))
+    return true;
+  // TODO: Some instructions are guaranteed to return neither undef
+  // nor poison if their arguments are not poison/undef.
+
+  // TODO: Deal with other Constant subclasses.
+  if (isa<ConstantInt>(V) || isa<GlobalVariable>(V))
+    return true;
+
+  return false;
+}
 
 OverflowResult llvm::computeOverflowForSignedAdd(const AddOperator *Add,
                                                  const DataLayout &DL,
diff --git a/llvm/lib/Transforms/InstCombine/InstCombineInternal.h b/llvm/lib/Transforms/InstCombine/InstCombineInternal.h
--- a/llvm/lib/Transforms/InstCombine/InstCombineInternal.h
+++ b/llvm/lib/Transforms/InstCombine/InstCombineInternal.h
@@ -446,6 +446,7 @@
   Instruction *visitLandingPadInst(LandingPadInst &LI);
   Instruction *visitVAStartInst(VAStartInst &I);
   Instruction *visitVACopyInst(VACopyInst &I);
+  Instruction *visitFreeze(FreezeInst &I);
 
   /// Specify what to return for unhandled instructions.
   Instruction *visitInstruction(Instruction &I) { return nullptr; }
diff --git a/llvm/lib/Transforms/InstCombine/InstructionCombining.cpp b/llvm/lib/Transforms/InstCombine/InstructionCombining.cpp
--- a/llvm/lib/Transforms/InstCombine/InstructionCombining.cpp
+++ b/llvm/lib/Transforms/InstCombine/InstructionCombining.cpp
@@ -3131,6 +3131,15 @@
   return nullptr;
 }
 
+Instruction *InstCombiner::visitFreeze(FreezeInst &I) {
+  Value *Op0 = I.getOperand(0);
+
+  if (Value *V = SimplifyFreezeInst(Op0, SQ.getWithInstruction(&I)))
+    return replaceInstUsesWith(I, V);
+
+  return nullptr;
+}
+
 /// Try to move the specified instruction from its current block into the
 /// beginning of DestBlock, which can only happen if it's safe to move the
 /// instruction past all of the instructions between it and the end of its
diff --git a/llvm/test/Transforms/InstCombine/freeze.ll b/llvm/test/Transforms/InstCombine/freeze.ll
new file mode 100644
--- /dev/null
+++ b/llvm/test/Transforms/InstCombine/freeze.ll
@@ -0,0 +1,20 @@
+; NOTE: Assertions have been autogenerated by utils/update_test_checks.py
+; RUN: opt < %s -instcombine -S | FileCheck %s
+
+define i32 @fold(i32 %x) {
+; CHECK-LABEL: @fold(
+; CHECK-NEXT:    [[Y:%.*]] = freeze i32 [[X:%.*]]
+; CHECK-NEXT:    ret i32 [[Y]]
+;
+  %y = freeze i32 %x
+  %z = freeze i32 %y
+  ret i32 %z
+}
+
+define i32 @make_const() {
+; CHECK-LABEL: @make_const(
+; CHECK-NEXT:    ret i32 10
+;
+  %x = freeze i32 10
+  ret i32 %x
+}
diff --git a/llvm/test/Transforms/InstSimplify/freeze.ll b/llvm/test/Transforms/InstSimplify/freeze.ll
new file mode 100644
--- /dev/null
+++ b/llvm/test/Transforms/InstSimplify/freeze.ll
@@ -0,0 +1,20 @@
+; NOTE: Assertions have been autogenerated by utils/update_test_checks.py
+; RUN: opt < %s -instsimplify -S | FileCheck %s
+
+define i32 @fold(i32 %x) {
+; CHECK-LABEL: @fold(
+; CHECK-NEXT:    [[Y:%.*]] = freeze i32 [[X:%.*]]
+; CHECK-NEXT:    ret i32 [[Y]]
+;
+  %y = freeze i32 %x
+  %z = freeze i32 %y
+  ret i32 %z
+}
+
+define i32 @make_const() {
+; CHECK-LABEL: @make_const(
+; CHECK-NEXT:    ret i32 10
+;
+  %x = freeze i32 10
+  ret i32 %x
+}