diff --git a/mlir/lib/IR/AffineExpr.cpp b/mlir/lib/IR/AffineExpr.cpp
--- a/mlir/lib/IR/AffineExpr.cpp
+++ b/mlir/lib/IR/AffineExpr.cpp
@@ -829,6 +829,16 @@
       return lBin.getLHS() % rhsConst.getValue();
   }
 
+  // Simplify (e % a) % b to e % b when b evenly divides a
+  // Note, this may not be valid if we ever allow negative modulus constants
+  if (lBin && lBin.getKind() == AffineExprKind::Mod) {
+    auto intermediate = lBin.getRHS().dyn_cast<AffineConstantExpr>();
+    if (intermediate &&
+        mod(intermediate.getValue(), rhsConst.getValue()) == 0) {
+      return lBin.getLHS() % rhsConst.getValue();
+    }
+  }
+
   return nullptr;
 }
 
diff --git a/mlir/test/IR/affine-map.mlir b/mlir/test/IR/affine-map.mlir
--- a/mlir/test/IR/affine-map.mlir
+++ b/mlir/test/IR/affine-map.mlir
@@ -189,6 +189,9 @@
 // CHECK: #map{{[0-9]+}} = affine_map<(d0, d1) -> (d0 * 3, (d0 + d1) * 2, d0 mod 2)>
 #map58 = affine_map<(d0, d1) -> (4*d0 - 2*d0 + d0, (d0 + d1) + (d0 + d1), 2 * (d0 mod 2) - d0 mod 2)>
 
+// CHECK: #map{{[0-9]+}} = affine_map<(d0, d1) -> (d0 mod 5, (d1 mod 35) mod 4)>
+#map59 = affine_map<(d0, d1) -> ((d0 mod 35) mod 5, (d1 mod 35) mod 4)>
+
 // Single identity maps are removed.
 // CHECK: @f0(memref<2x4xi8, 1>)
 func private @f0(memref<2x4xi8, #map0, 1>)
@@ -373,3 +376,6 @@
 
 // CHECK: "f58"() {map = #map{{[0-9]+}}} : () -> ()
 "f58"() {map = #map58} : () -> ()
+
+// CHECK: "f59"() {map = #map{{[0-9]+}}} : () -> ()
+"f59"() {map = #map59} : () -> ()
\ No newline at end of file
diff --git a/mlir/test/Transforms/loop-fusion-2.mlir b/mlir/test/Transforms/loop-fusion-2.mlir
--- a/mlir/test/Transforms/loop-fusion-2.mlir
+++ b/mlir/test/Transforms/loop-fusion-2.mlir
@@ -1,7 +1,7 @@
 // RUN: mlir-opt -allow-unregistered-dialect %s -affine-loop-fusion -split-input-file | FileCheck %s
 // RUN: mlir-opt -allow-unregistered-dialect %s -affine-loop-fusion="fusion-maximal" -split-input-file | FileCheck %s --check-prefix=MAXIMAL
 
-// Part I of fusion tests in  mlir/test/Transforms/loop-fusion.mlir. 
+// Part I of fusion tests in  mlir/test/Transforms/loop-fusion.mlir.
 // Part III of fusion tests in mlir/test/Transforms/loop-fusion-3.mlir
 // Part IV of fusion tests in mlir/test/Transforms/loop-fusion-4.mlir
 
@@ -576,9 +576,9 @@
 }
 // MAXIMAL-DAG: [[$MAP0:#map[0-9]+]] = affine_map<(d0, d1) -> ((d0 * 72 + d1) floordiv 2304)>
 // MAXIMAL-DAG: [[$MAP1:#map[0-9]+]] = affine_map<(d0, d1) -> (((d0 * 72 + d1) mod 2304) floordiv 1152)>
-// MAXIMAL-DAG: [[$MAP2:#map[0-9]+]] = affine_map<(d0, d1) -> (((((d0 * 72 + d1) mod 2304) mod 1152) floordiv 9) floordiv 8)>
-// MAXIMAL-DAG: [[$MAP3:#map[0-9]+]] = affine_map<(d0, d1) -> (((((d0 * 72 + d1) mod 2304) mod 1152) mod 9) floordiv 3)>
-// MAXIMAL-DAG: [[$MAP4:#map[0-9]+]] = affine_map<(d0, d1) -> (((((d0 * 72 + d1) mod 2304) mod 1152) mod 9) mod 3)>
+// MAXIMAL-DAG: [[$MAP2:#map[0-9]+]] = affine_map<(d0, d1) -> ((((d0 * 72 + d1) mod 1152) floordiv 9) floordiv 8)>
+// MAXIMAL-DAG: [[$MAP3:#map[0-9]+]] = affine_map<(d0, d1) -> ((d1 mod 9) floordiv 3)>
+// MAXIMAL-DAG: [[$MAP4:#map[0-9]+]] = affine_map<(d0, d1) -> (d1 mod 3)>
 // MAXIMAL-DAG: [[$MAP7:#map[0-9]+]] = affine_map<(d0, d1) -> (d0 * 16 + d1)>
 // MAXIMAL-DAG: [[$MAP8:#map[0-9]+]] = affine_map<(d0, d1) -> (d0 * 16 - d1 + 15)>
 // MAXIMAL-LABEL: func @fuse_across_varying_dims_complex
diff --git a/mlir/test/Transforms/loop-fusion.mlir b/mlir/test/Transforms/loop-fusion.mlir
--- a/mlir/test/Transforms/loop-fusion.mlir
+++ b/mlir/test/Transforms/loop-fusion.mlir
@@ -1,6 +1,6 @@
 // RUN: mlir-opt -allow-unregistered-dialect %s -affine-loop-fusion -split-input-file | FileCheck %s
 
-// Part II of fusion tests in  mlir/test/Transforms/loop-fusion=2.mlir. 
+// Part II of fusion tests in  mlir/test/Transforms/loop-fusion=2.mlir.
 // Part III of fusion tests in mlir/test/Transforms/loop-fusion-3.mlir
 // Part IV of fusion tests in mlir/test/Transforms/loop-fusion-4.mlir
 
@@ -737,15 +737,15 @@
 //
 // CHECK-DAG: [[$MAP0:#map[0-9]+]] = affine_map<(d0, d1) -> ((d0 * 9 + d1) floordiv 288)>
 // CHECK-DAG: [[$MAP1:#map[0-9]+]] = affine_map<(d0, d1) -> (((d0 * 9 + d1) mod 288) floordiv 144)>
-// CHECK-DAG: [[$MAP2:#map[0-9]+]] = affine_map<(d0, d1) -> ((((d0 * 9 + d1) mod 288) mod 144) floordiv 48)>
-// CHECK-DAG: [[$MAP3:#map[0-9]+]] = affine_map<(d0, d1) -> (((((d0 * 9 + d1) mod 288) mod 144) mod 48) floordiv 16)>
-// CHECK-DAG: [[$MAP4:#map[0-9]+]] = affine_map<(d0, d1) -> (((((d0 * 9 + d1) mod 288) mod 144) mod 48) mod 16)>
+// CHECK-DAG: [[$MAP2:#map[0-9]+]] = affine_map<(d0, d1) -> (((d0 * 9 + d1) mod 144) floordiv 48)>
+// CHECK-DAG: [[$MAP3:#map[0-9]+]] = affine_map<(d0, d1) -> (((d0 * 9 + d1) mod 48) floordiv 16)>
+// CHECK-DAG: [[$MAP4:#map[0-9]+]] = affine_map<(d0, d1) -> ((d0 * 9 + d1) mod 16)>
 // CHECK-DAG: [[$MAP11:#map[0-9]+]] = affine_map<(d0, d1) -> (d0 * 9 + d1)>
 // CHECK-DAG: [[$MAP12:#map[0-9]+]] = affine_map<(d0) -> (d0 floordiv 288)>
 // CHECK-DAG: [[$MAP13:#map[0-9]+]] = affine_map<(d0) -> ((d0 mod 288) floordiv 144)>
-// CHECK-DAG: [[$MAP14:#map[0-9]+]] = affine_map<(d0) -> (((d0 mod 288) mod 144) floordiv 48)>
-// CHECK-DAG: [[$MAP15:#map[0-9]+]] = affine_map<(d0) -> ((((d0 mod 288) mod 144) mod 48) floordiv 16)>
-// CHECK-DAG: [[$MAP16:#map[0-9]+]] = affine_map<(d0) -> ((((d0 mod 288) mod 144) mod 48) mod 16)>
+// CHECK-DAG: [[$MAP14:#map[0-9]+]] = affine_map<(d0) -> ((d0 mod 144) floordiv 48)>
+// CHECK-DAG: [[$MAP15:#map[0-9]+]] = affine_map<(d0) -> ((d0 mod 48) floordiv 16)>
+// CHECK-DAG: [[$MAP16:#map[0-9]+]] = affine_map<(d0) -> (d0 mod 16)>
 // CHECK-DAG: [[$MAP17:#map[0-9]+]] = affine_map<(d0) -> (0)>
 
 //
@@ -761,7 +761,7 @@
 // CHECK-NEXT:      affine.apply [[$MAP3]](%{{.*}}, %{{.*}})
 // CHECK-NEXT:      affine.apply [[$MAP4]](%{{.*}}, %{{.*}})
 // CHECK-NEXT:      "foo"(%{{.*}}, %{{.*}}, %{{.*}}, %{{.*}}, %{{.*}}, %{{.*}}) : (index, index, index, index, index, index) -> i32
-// CHECK-NEXT:      affine.store %{{.*}}, %{{.*}}[0, ((%{{.*}} * 9 + %{{.*}}) mod 288) floordiv 144, (((%{{.*}} * 9 + %{{.*}}) mod 288) mod 144) floordiv 48, ((((%{{.*}} * 9 + %{{.*}}) mod 288) mod 144) mod 48) floordiv 16, ((((%{{.*}} * 9 + %{{.*}}) mod 288) mod 144) mod 48) mod 16, 0] : memref<1x2x3x3x16x1xi32>
+// CHECK-NEXT:      affine.store %{{.*}}, %{{.*}}[0, ((%{{.*}} * 9 + %{{.*}}) mod 288) floordiv 144, ((%{{.*}} * 9 + %{{.*}}) mod 144) floordiv 48, ((%{{.*}} * 9 + %{{.*}}) mod 48) floordiv 16, (%{{.*}} * 9 + %{{.*}}) mod 16, 0] : memref<1x2x3x3x16x1xi32>
 // CHECK-NEXT:      affine.apply [[$MAP11]](%{{.*}}, %{{.*}})
 // CHECK-NEXT:      affine.apply [[$MAP12]](%{{.*}})
 // CHECK-NEXT:      affine.apply [[$MAP13]](%{{.*}})
@@ -769,7 +769,7 @@
 // CHECK-NEXT:      affine.apply [[$MAP15]](%{{.*}})
 // CHECK-NEXT:      affine.apply [[$MAP16]](%{{.*}})
 // CHECK-NEXT:      affine.apply [[$MAP17]](%{{.*}})
-// CHECK-NEXT:      affine.load %{{.*}}[0, ((%{{.*}} * 9 + %{{.*}}) mod 288) floordiv 144, (((%{{.*}} * 9 + %{{.*}}) mod 288) mod 144) floordiv 48, ((((%{{.*}} * 9 + %{{.*}}) mod 288) mod 144) mod 48) floordiv 16, ((((%{{.*}} * 9 + %{{.*}}) mod 288) mod 144) mod 48) mod 16, 0] : memref<1x2x3x3x16x1xi32>
+// CHECK-NEXT:      affine.load %{{.*}}[0, ((%{{.*}} * 9 + %{{.*}}) mod 288) floordiv 144, ((%{{.*}} * 9 + %{{.*}}) mod 144) floordiv 48, ((%{{.*}} * 9 + %{{.*}}) mod 48) floordiv 16, (%{{.*}} * 9 + %{{.*}}) mod 16, 0] : memref<1x2x3x3x16x1xi32>
 // CHECK-NEXT:      affine.store %{{.*}}, %{{.*}}[0, 0] : memref<1x1xi32>
 // CHECK-NEXT:      affine.load %{{.*}}[0, 0] : memref<1x1xi32>
 // CHECK-NEXT:      muli %{{.*}}, %{{.*}} : i32