diff --git a/mlir/include/mlir/Dialect/Affine/Analysis/AffineStructures.h b/mlir/include/mlir/Dialect/Affine/Analysis/AffineStructures.h
--- a/mlir/include/mlir/Dialect/Affine/Analysis/AffineStructures.h
+++ b/mlir/include/mlir/Dialect/Affine/Analysis/AffineStructures.h
@@ -24,6 +24,7 @@
 class AffineCondition;
 class AffineForOp;
 class AffineIfOp;
+class AffineParallelOp;
 class AffineMap;
 class AffineValueMap;
 class IntegerSet;
@@ -141,6 +142,13 @@
   //  TODO: add support for non-unit strides.
   LogicalResult addAffineForOpDomain(AffineForOp forOp);
 
+  /// Add constraints (lower and upper bounds) for the specified
+  /// 'affine.parallel' operation's Value using IR information stored in its
+  /// bound maps. Returns failure for the yet unimplemented/unsupported cases.
+  /// Asserts if the Value corresponding to the 'affine.parallel' operation
+  /// isn't found in the constraint system.
+  LogicalResult addAffineParallelOpDomain(AffineParallelOp parallelOp);
+
   /// Adds constraints (lower and upper bounds) for each loop in the loop nest
   /// described by the bound maps `lbMaps` and `ubMaps` of a computation slice.
   /// Every pair (`lbMaps[i]`, `ubMaps[i]`) describes the bounds of a loop in
diff --git a/mlir/include/mlir/Dialect/Affine/IR/AffineOps.h b/mlir/include/mlir/Dialect/Affine/IR/AffineOps.h
--- a/mlir/include/mlir/Dialect/Affine/IR/AffineOps.h
+++ b/mlir/include/mlir/Dialect/Affine/IR/AffineOps.h
@@ -45,6 +45,10 @@
 /// trait `AffineScope`; `nullptr` if there is no such region.
 Region *getAffineScope(Operation *op);
 
+/// Returns whether the op is within an affine parallel op which can potentially
+/// preventing the dependence analysis.
+bool isInParallelOp(Operation *op);
+
 /// AffineDmaStartOp starts a non-blocking DMA operation that transfers data
 /// from a source memref to a destination memref. The source and destination
 /// memref need not be of the same dimensionality, but need to have the same
@@ -450,6 +454,11 @@
 void extractForInductionVars(ArrayRef<AffineForOp> forInsts,
                              SmallVectorImpl<Value> *ivs);
 
+/// Extracts the induction variables from a list of either AffineForOp or
+/// AffineParallelOp and places them in the output argument `ivs`.
+void extractInductionVars(ArrayRef<Operation *> operations,
+                          SmallVectorImpl<Value> *ivs);
+
 /// Builds a perfect nest of affine.for loops, i.e., each loop except the
 /// innermost one contains only another loop and a terminator. The loops iterate
 /// from "lbs" to "ubs" with "steps". The body of the innermost loop is
diff --git a/mlir/lib/Dialect/Affine/Analysis/AffineAnalysis.cpp b/mlir/lib/Dialect/Affine/Analysis/AffineAnalysis.cpp
--- a/mlir/lib/Dialect/Affine/Analysis/AffineAnalysis.cpp
+++ b/mlir/lib/Dialect/Affine/Analysis/AffineAnalysis.cpp
@@ -240,19 +240,26 @@
 LogicalResult mlir::getIndexSet(MutableArrayRef<Operation *> ops,
                                 FlatAffineValueConstraints *domain) {
   SmallVector<Value, 4> indices;
-  SmallVector<AffineForOp, 8> forOps;
+  SmallVector<Operation *, 8> loopOps;
+  size_t numDims = 0;
   for (Operation *op : ops) {
-    if (!isa<AffineForOp, AffineIfOp>(op)) {
-      // TODO: Support affine.parallel ops.
-      LLVM_DEBUG(llvm::dbgs() << "getIndexSet only handles affine.for/if ops");
+    if (!isa<AffineForOp, AffineIfOp, AffineParallelOp>(op)) {
+      LLVM_DEBUG(llvm::dbgs() << "getIndexSet only handles affine.for/if/"
+                                 "parallel ops");
       return failure();
     }
-    if (AffineForOp forOp = dyn_cast<AffineForOp>(op))
-      forOps.push_back(forOp);
+    if (AffineForOp forOp = dyn_cast<AffineForOp>(op)) {
+      loopOps.push_back(forOp);
+      // An AffineForOp retains only 1 induction variable.
+      numDims += 1;
+    } else if (AffineParallelOp parallelOp = dyn_cast<AffineParallelOp>(op)) {
+      loopOps.push_back(parallelOp);
+      numDims += parallelOp.getNumDims();
+    }
   }
-  extractForInductionVars(forOps, &indices);
-  // Reset while associated Values in 'indices' to the domain.
-  domain->reset(forOps.size(), /*numSymbols=*/0, /*numLocals=*/0, indices);
+  extractInductionVars(loopOps, &indices);
+  // Reset while associating Values in 'indices' to the domain.
+  domain->reset(numDims, /*numSymbols=*/0, /*numLocals=*/0, indices);
   for (Operation *op : ops) {
     // Add constraints from forOp's bounds.
     if (AffineForOp forOp = dyn_cast<AffineForOp>(op)) {
@@ -260,7 +267,9 @@
         return failure();
     } else if (AffineIfOp ifOp = dyn_cast<AffineIfOp>(op)) {
       domain->addAffineIfOpDomain(ifOp);
-    }
+    } else if (AffineParallelOp parallelOp = dyn_cast<AffineParallelOp>(op))
+      if (failed(domain->addAffineParallelOpDomain(parallelOp)))
+        return failure();
   }
   return success();
 }
@@ -604,6 +613,10 @@
   if (getAffineScope(srcAccess.opInst) != getAffineScope(dstAccess.opInst))
     return DependenceResult::Failure;
 
+  // TODO: Support affine.parallel which does not specify the ordering.
+  if (isInParallelOp(srcAccess.opInst) || isInParallelOp(dstAccess.opInst))
+    return DependenceResult::Failure;
+
   // Create access relation from each MemRefAccess.
   FlatAffineRelation srcRel, dstRel;
   if (failed(srcAccess.getAccessRelation(srcRel)))
diff --git a/mlir/lib/Dialect/Affine/Analysis/AffineStructures.cpp b/mlir/lib/Dialect/Affine/Analysis/AffineStructures.cpp
--- a/mlir/lib/Dialect/Affine/Analysis/AffineStructures.cpp
+++ b/mlir/lib/Dialect/Affine/Analysis/AffineStructures.cpp
@@ -639,6 +639,34 @@
                   forOp.getUpperBoundOperands());
 }
 
+LogicalResult FlatAffineValueConstraints::addAffineParallelOpDomain(
+    AffineParallelOp parallelOp) {
+  size_t ivPos = 0;
+  for (auto iv : parallelOp.getIVs()) {
+    LLVM_DEBUG(iv.dump(););
+    unsigned pos;
+    if (!findVar(iv, &pos)) {
+      assert(false && "variable expected for the IV value");
+      return failure();
+    }
+
+    AffineMap lowerBound = parallelOp.getLowerBoundMap(ivPos);
+    if (lowerBound.isConstant())
+      addBound(BoundType::LB, pos, lowerBound.getSingleConstantResult());
+    else if (failed(addBound(BoundType::LB, pos, lowerBound,
+                             parallelOp.getLowerBoundsOperands())))
+      return failure();
+
+    auto upperBound = parallelOp.getUpperBoundMap(ivPos);
+    if (upperBound.isConstant())
+      addBound(BoundType::UB, pos, upperBound.getSingleConstantResult());
+    else if (failed(addBound(BoundType::UB, pos, upperBound,
+                             parallelOp.getUpperBoundsOperands())))
+      return failure();
+  }
+  return success();
+}
+
 LogicalResult
 FlatAffineValueConstraints::addDomainFromSliceMaps(ArrayRef<AffineMap> lbMaps,
                                                    ArrayRef<AffineMap> ubMaps,
diff --git a/mlir/lib/Dialect/Affine/IR/AffineOps.cpp b/mlir/lib/Dialect/Affine/IR/AffineOps.cpp
--- a/mlir/lib/Dialect/Affine/IR/AffineOps.cpp
+++ b/mlir/lib/Dialect/Affine/IR/AffineOps.cpp
@@ -254,6 +254,16 @@
   return nullptr;
 }
 
+bool mlir::isInParallelOp(mlir::Operation *op) {
+  auto *curOp = op;
+  while (auto *parentOp = curOp->getParentOp()) {
+    if (isa<AffineParallelOp>(parentOp))
+      return true;
+    curOp = parentOp;
+  }
+  return false;
+}
+
 // A Value can be used as a dimension id iff it meets one of the following
 // conditions:
 // *) It is valid as a symbol.
@@ -2311,6 +2321,19 @@
     ivs->push_back(forInst.getInductionVar());
 }
 
+void mlir::extractInductionVars(ArrayRef<mlir::Operation *> operations,
+                                SmallVectorImpl<mlir::Value> *ivs) {
+  ivs->reserve(operations.size());
+  for (Operation *op : operations) {
+    // Add constraints from forOp's bounds.
+    if (AffineForOp forOp = dyn_cast<AffineForOp>(op))
+      ivs->push_back(forOp.getInductionVar());
+    else if (AffineParallelOp parallelOp = dyn_cast<AffineParallelOp>(op))
+      for (size_t i = 0; i < parallelOp.getBody()->getNumArguments(); i++)
+        ivs->push_back(parallelOp.getBody()->getArgument(i));
+  }
+}
+
 /// Builds an affine loop nest, using "loopCreatorFn" to create individual loop
 /// operations.
 template <typename BoundListTy, typename LoopCreatorTy>