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
@@ -992,6 +992,29 @@
   return ::simplifyMulInst(Op0, Op1, IsNSW, IsNUW, Q, RecursionLimit);
 }
 
+Value *simplifyRemShifts(Value *Op0, Value *Op1, bool IsSigned,
+                         const SimplifyQuery &Q) {
+  // rem X << S1, X << S2
+  // if (S1 >= S2) -> 0; else -> X << S1
+  Value *ShiftX;
+  ConstantInt *S1, *S2;
+  if (!match(Op0, m_Shl(m_Value(ShiftX), m_ConstantInt(S1))) ||
+      !match(Op1, m_Shl(m_Deferred(ShiftX), m_ConstantInt(S2))))
+    return nullptr;
+
+  auto Shift = cast<OverflowingBinaryOperator>(Op0);
+  if (S1 >= S2 && ((IsSigned && Q.IIQ.hasNoSignedWrap(Shift)) ||
+                   (!IsSigned && Q.IIQ.hasNoUnsignedWrap(Shift))))
+    return Constant::getNullValue(Shift->getType());
+
+  Shift = cast<OverflowingBinaryOperator>(Op1);
+  if ((IsSigned && Q.IIQ.hasNoSignedWrap(Shift)) ||
+      (!IsSigned && Q.IIQ.hasNoUnsignedWrap(Shift)))
+    return Op0;
+
+  return nullptr;
+}
+
 /// Check for common or similar folds of integer division or integer remainder.
 /// This applies to all 4 opcodes (sdiv/udiv/srem/urem).
 static Value *simplifyDivRem(Instruction::BinaryOps Opcode, Value *Op0,
@@ -1074,6 +1097,9 @@
   if (Value *V = simplifyByDomEq(Opcode, Op0, Op1, Q, MaxRecurse))
     return V;
 
+  if (!IsDiv)
+    if (Value *V = simplifyRemShifts(Op0, Op1, IsSigned, Q))
+      return V;
   return nullptr;
 }
 
diff --git a/llvm/test/Transforms/InstSimplify/rem.ll b/llvm/test/Transforms/InstSimplify/rem.ll
--- a/llvm/test/Transforms/InstSimplify/rem.ll
+++ b/llvm/test/Transforms/InstSimplify/rem.ll
@@ -488,3 +488,97 @@
   %mod = urem i8 %mul, %y
   ret i8 %mod
 }
+
+define i8 @urem_shl(i8 %x){
+; CHECK-LABEL: @urem_shl(
+; CHECK-NEXT:    ret i8 0
+;
+  %x1 = shl i8 %x, 1
+  %x2 = shl nuw i8 %x, 2
+  %1 = urem i8 %x2, %x1
+  ret i8 %1
+}
+
+define i8 @neg_urem_shl(i8 %x){
+; CHECK-LABEL: @neg_urem_shl(
+; CHECK-NEXT:    [[X1:%.*]] = shl i8 [[X:%.*]], 1
+; CHECK-NEXT:    [[X2:%.*]] = shl i8 [[X]], 2
+; CHECK-NEXT:    [[TMP1:%.*]] = urem i8 [[X2]], [[X1]]
+; CHECK-NEXT:    ret i8 [[TMP1]]
+;
+  %x1 = shl i8 %x, 1
+  %x2 = shl i8 %x, 2
+  %1 = urem i8 %x2, %x1
+  ret i8 %1
+}
+
+define i8 @urem_shl_2(i8 %x){
+; CHECK-LABEL: @urem_shl_2(
+; CHECK-NEXT:    [[X1:%.*]] = shl i8 [[X:%.*]], 1
+; CHECK-NEXT:    ret i8 [[X1]]
+;
+  %x1 = shl i8 %x, 1
+  %x2 = shl nuw i8 %x, 2
+  %1 = urem i8 %x1, %x2
+  ret i8 %1
+}
+
+define i8 @neg_urem_shl_2(i8 %x){
+; CHECK-LABEL: @neg_urem_shl_2(
+; CHECK-NEXT:    [[X1:%.*]] = shl i8 [[X:%.*]], 1
+; CHECK-NEXT:    [[X2:%.*]] = shl i8 [[X]], 2
+; CHECK-NEXT:    [[TMP1:%.*]] = urem i8 [[X1]], [[X2]]
+; CHECK-NEXT:    ret i8 [[TMP1]]
+;
+  %x1 = shl i8 %x, 1
+  %x2 = shl i8 %x, 2
+  %1 = urem i8 %x1, %x2
+  ret i8 %1
+}
+
+define i8 @srem_shl(i8 %x){
+; CHECK-LABEL: @srem_shl(
+; CHECK-NEXT:    ret i8 0
+;
+  %x1 = shl i8 %x, 1
+  %x2 = shl nsw i8 %x, 2
+  %1 = srem i8 %x2, %x1
+  ret i8 %1
+}
+
+define i8 @neg_srem_shl(i8 %x){
+; CHECK-LABEL: @neg_srem_shl(
+; CHECK-NEXT:    [[X1:%.*]] = shl i8 [[X:%.*]], 1
+; CHECK-NEXT:    [[X2:%.*]] = shl i8 [[X]], 2
+; CHECK-NEXT:    [[TMP1:%.*]] = srem i8 [[X2]], [[X1]]
+; CHECK-NEXT:    ret i8 [[TMP1]]
+;
+  %x1 = shl i8 %x, 1
+  %x2 = shl i8 %x, 2
+  %1 = srem i8 %x2, %x1
+  ret i8 %1
+}
+
+define i8 @srem_shl_2(i8 %x){
+; CHECK-LABEL: @srem_shl_2(
+; CHECK-NEXT:    [[X1:%.*]] = shl i8 [[X:%.*]], 1
+; CHECK-NEXT:    [[X2:%.*]] = shl i8 [[X]], 2
+; CHECK-NEXT:    [[TMP1:%.*]] = srem i8 [[X1]], [[X2]]
+; CHECK-NEXT:    ret i8 [[TMP1]]
+;
+  %x1 = shl i8 %x, 1
+  %x2 = shl i8 %x, 2
+  %1 = srem i8 %x1, %x2
+  ret i8 %1
+}
+
+define i8 @neg_srem_shl_2(i8 %x){
+; CHECK-LABEL: @neg_srem_shl_2(
+; CHECK-NEXT:    [[X1:%.*]] = shl i8 [[X:%.*]], 1
+; CHECK-NEXT:    ret i8 [[X1]]
+;
+  %x1 = shl i8 %x, 1
+  %x2 = shl nsw i8 %x, 2
+  %1 = srem i8 %x1, %x2
+  ret i8 %1
+}