diff --git a/flang/lib/Lower/OpenACC.cpp b/flang/lib/Lower/OpenACC.cpp
--- a/flang/lib/Lower/OpenACC.cpp
+++ b/flang/lib/Lower/OpenACC.cpp
@@ -584,24 +584,52 @@
                                          mlir::acc::ReductionOperator op) {
   if (op != mlir::acc::ReductionOperator::AccAdd &&
       op != mlir::acc::ReductionOperator::AccMul &&
-      op != mlir::acc::ReductionOperator::AccMin)
+      op != mlir::acc::ReductionOperator::AccMin &&
+      op != mlir::acc::ReductionOperator::AccMax)
     TODO(loc, "reduction operator");
 
-  // 0 for +, ior, ieor
-  // 1 for *
-  int64_t initValue = op == mlir::acc::ReductionOperator::AccMul ? 1 : 0;
-
+  // min -> largest
   if (op == mlir::acc::ReductionOperator::AccMin) {
-    unsigned bits = ty.getIntOrFloatBitWidth();
-    initValue = llvm::APInt::getSignedMinValue(bits).getSExtValue();
+    if (ty.isIntOrIndex()) {
+      unsigned bits = ty.getIntOrFloatBitWidth();
+      return builder.create<mlir::arith::ConstantOp>(
+          loc, ty,
+          builder.getIntegerAttr(
+              ty, llvm::APInt::getSignedMaxValue(bits).getSExtValue()));
+    }
+    if (auto floatTy = mlir::dyn_cast_or_null<mlir::FloatType>(ty)) {
+      const llvm::fltSemantics &sem = floatTy.getFloatSemantics();
+      return builder.create<mlir::arith::ConstantOp>(
+          loc, ty,
+          builder.getFloatAttr(
+              ty, llvm::APFloat::getLargest(sem, /*negative=*/false)));
+    }
+    // max -> least
+  } else if (op == mlir::acc::ReductionOperator::AccMax) {
+    if (ty.isIntOrIndex())
+      return builder.create<mlir::arith::ConstantOp>(
+          loc, ty,
+          builder.getIntegerAttr(
+              ty, llvm::APInt::getSignedMinValue(ty.getIntOrFloatBitWidth())
+                      .getSExtValue()));
+    if (auto floatTy = mlir::dyn_cast_or_null<mlir::FloatType>(ty))
+      return builder.create<mlir::arith::ConstantOp>(
+          loc, ty,
+          builder.getFloatAttr(
+              ty, llvm::APFloat::getSmallest(floatTy.getFloatSemantics(),
+                                             /*negative=*/true)));
+  } else {
+    // 0 for +, ior, ieor
+    // 1 for *
+    int64_t initValue = op == mlir::acc::ReductionOperator::AccMul ? 1 : 0;
+    if (ty.isIntOrIndex())
+      return builder.create<mlir::arith::ConstantOp>(
+          loc, ty, builder.getIntegerAttr(ty, initValue));
+    if (mlir::isa<mlir::FloatType>(ty))
+      return builder.create<mlir::arith::ConstantOp>(
+          loc, ty, builder.getFloatAttr(ty, initValue));
   }
 
-  if (ty.isIntOrIndex())
-    return builder.create<mlir::arith::ConstantOp>(
-        loc, ty, builder.getIntegerAttr(ty, initValue));
-  if (mlir::isa<mlir::FloatType>(ty))
-    return builder.create<mlir::arith::ConstantOp>(
-        loc, ty, builder.getFloatAttr(ty, initValue));
   TODO(loc, "reduction type");
 }
 
@@ -624,16 +652,27 @@
     TODO(loc, "reduction mul type");
   }
 
-  if (op == mlir::acc::ReductionOperator::AccMin) {
+  if (op == mlir::acc::ReductionOperator::AccMin ||
+      op == mlir::acc::ReductionOperator::AccMax) {
     mlir::Value cmp;
-    if (ty.isIntOrIndex())
-      cmp = builder.create<mlir::arith::CmpIOp>(loc, mlir::arith::CmpIPredicate::slt, value1, value2);
-    if (mlir::isa<mlir::FloatType>(ty))
-      cmp = builder.create<mlir::arith::CmpFOp>(loc, mlir::arith::CmpFPredicate::OLT, value1, value2);
+    if (ty.isIntOrIndex()) {
+      mlir::arith::CmpIPredicate predicate =
+          op == mlir::acc::ReductionOperator::AccMin
+              ? mlir::arith::CmpIPredicate::slt
+              : mlir::arith::CmpIPredicate::sgt;
+      cmp = builder.create<mlir::arith::CmpIOp>(loc, predicate, value1, value2);
+    }
+    if (mlir::isa<mlir::FloatType>(ty)) {
+      mlir::arith::CmpFPredicate predicate =
+          op == mlir::acc::ReductionOperator::AccMin
+              ? mlir::arith::CmpFPredicate::OLT
+              : mlir::arith::CmpFPredicate::OGT;
+      cmp = builder.create<mlir::arith::CmpFOp>(loc, predicate, value1, value2);
+    }
     if (cmp)
       return builder.create<mlir::arith::SelectOp>(loc, cmp, value1, value2);
-    
-    TODO(loc, "reduction mul type");
+
+    TODO(loc, "reduction min/max type");
   }
 
   TODO(loc, "reduction operator");
diff --git a/flang/test/Lower/OpenACC/acc-reduction.f90 b/flang/test/Lower/OpenACC/acc-reduction.f90
--- a/flang/test/Lower/OpenACC/acc-reduction.f90
+++ b/flang/test/Lower/OpenACC/acc-reduction.f90
@@ -2,9 +2,31 @@
 
 ! RUN: bbc -fopenacc -emit-fir %s -o - | FileCheck %s
 
+! CHECK-LABEL: acc.reduction.recipe @reduction_max_f32 : f32 reduction_operator <max> init {
+! CHECK: ^bb0(%{{.*}}: f32):
+! CHECK:   %[[INIT:.*]] = arith.constant -1.401300e-45 : f32
+! CHECK:   acc.yield %[[INIT]] : f32
+! CHECK: } combiner {
+! CHECK: ^bb0(%[[ARG0:.*]]: f32, %[[ARG1:.*]]: f32):
+! CHECK:   %[[CMP:.*]] = arith.cmpf ogt, %[[ARG0]], %[[ARG1]] : f32
+! CHECK:   %[[SELECT:.*]] = arith.select %[[CMP]], %[[ARG0]], %[[ARG1]] : f32
+! CHECK:   acc.yield %[[SELECT]] : f32
+! CHECK: }
+
+! CHECK-LABEL: acc.reduction.recipe @reduction_max_i32 : i32 reduction_operator <max> init {
+! CHECK: ^bb0(%arg0: i32):
+! CHECK:   %[[INIT:.*]] = arith.constant -2147483648 : i32
+! CHECK:   acc.yield %[[INIT]] : i32
+! CHECK: } combiner {
+! CHECK: ^bb0(%[[ARG0:.*]]: i32, %[[ARG1:.*]]: i32):
+! CHECK:   %[[CMP:.*]] = arith.cmpi sgt, %[[ARG0]], %[[ARG1]] : i32
+! CHECK:   %[[SELECT:.*]] = arith.select %[[CMP]], %[[ARG0]], %[[ARG1]] : i32
+! CHECK:   acc.yield %[[SELECT]] : i32
+! CHECK: }
+
 ! CHECK-LABEL: acc.reduction.recipe @reduction_min_f32 : f32 reduction_operator <min> init {
 ! CHECK: ^bb0(%{{.*}}: f32):
-! CHECK:   %[[INIT:.*]] = arith.constant -2.14748365E+9 : f32
+! CHECK:   %[[INIT:.*]] = arith.constant 3.40282347E+38 : f32
 ! CHECK:   acc.yield %[[INIT]] : f32
 ! CHECK: } combiner {
 ! CHECK: ^bb0(%[[ARG0:.*]]: f32, %[[ARG1:.*]]: f32):
@@ -15,7 +37,7 @@
 
 ! CHECK-LABEL: acc.reduction.recipe @reduction_min_i32 : i32 reduction_operator <min> init {
 ! CHECK: ^bb0(%arg0: i32):
-! CHECK:   %[[INIT:.*]] = arith.constant -2147483648 : i32
+! CHECK:   %[[INIT:.*]] = arith.constant 2147483647 : i32
 ! CHECK:   acc.yield %[[INIT]] : i32
 ! CHECK: } combiner {
 ! CHECK: ^bb0(%[[ARG0:.*]]: i32, %[[ARG1:.*]]: i32):
@@ -148,3 +170,31 @@
 ! CHECK-LABEL: func.func @_QPacc_reduction_min_float(
 ! CHECK-SAME:  %{{.*}}: !fir.ref<!fir.array<100xf32>> {fir.bindc_name = "a"}, %[[B:.*]]: !fir.ref<f32> {fir.bindc_name = "b"})
 ! CHECK:       acc.loop reduction(@reduction_min_f32 -> %[[B]] : !fir.ref<f32>)
+
+subroutine acc_reduction_max_int(a, b)
+  integer :: a(100)
+  integer :: i, b
+
+  !$acc loop reduction(max:b)
+  do i = 1, 100
+    b = max(b, a(i))
+  end do
+end subroutine
+
+! CHECK-LABEL: func.func @_QPacc_reduction_max_int(
+! CHECK-SAME:  %{{.*}}: !fir.ref<!fir.array<100xi32>> {fir.bindc_name = "a"}, %[[B:.*]]: !fir.ref<i32> {fir.bindc_name = "b"})
+! CHECK:       acc.loop reduction(@reduction_max_i32 -> %[[B]] : !fir.ref<i32>)
+
+subroutine acc_reduction_max_float(a, b)
+  real :: a(100), b
+  integer :: i
+
+  !$acc loop reduction(max:b)
+  do i = 1, 100
+    b = max(b, a(i))
+  end do
+end subroutine
+
+! CHECK-LABEL: func.func @_QPacc_reduction_max_float(
+! CHECK-SAME:  %{{.*}}: !fir.ref<!fir.array<100xf32>> {fir.bindc_name = "a"}, %[[B:.*]]: !fir.ref<f32> {fir.bindc_name = "b"})
+! CHECK:       acc.loop reduction(@reduction_max_f32 -> %[[B]] : !fir.ref<f32>)