diff --git a/flang/include/flang/Runtime/io-api.h b/flang/include/flang/Runtime/io-api.h
--- a/flang/include/flang/Runtime/io-api.h
+++ b/flang/include/flang/Runtime/io-api.h
@@ -111,6 +111,24 @@
     void **scratchArea = nullptr, std::size_t scratchBytes = 0,
     const char *sourceFile = nullptr, int sourceLine = 0);
 
+// External unit numbers must fit in default integers. When the integer
+// provided as UNIT is of a wider type than the default integer, it could
+// overflow when converted to a default integer.
+// CheckUnitNumberInRange should be called to verify that a unit number of a
+// wide integer type can fit in a default integer. Since it should be called
+// before the BeginXXX(unit, ...) call, it has its own error handling interface.
+// If handleError is false, and the unit number is out of range, the program
+// will be terminated. Otherwise, if unit is out of range, a nonzero Iostat
+// code is returned and ioMsg is set if it is not a nullptr.
+enum Iostat IONAME(CheckUnitNumberInRange64)(std::int64_t unit,
+    bool handleError, char *ioMsg = nullptr, std::size_t ioMsgLength = 0,
+    const char *sourceFile = nullptr, int sourceLine = 0);
+#ifdef __SIZEOF_INT128__
+enum Iostat IONAME(CheckUnitNumberInRange128)(common::int128_t unit,
+    bool handleError, char *ioMsg = nullptr, std::size_t ioMsgLength = 0,
+    const char *sourceFile = nullptr, int sourceLine = 0);
+#endif
+
 // External synchronous I/O initiation
 Cookie IONAME(BeginExternalListOutput)(ExternalUnit = DefaultUnit,
     const char *sourceFile = nullptr, int sourceLine = 0);
diff --git a/flang/include/flang/Runtime/iostat.h b/flang/include/flang/Runtime/iostat.h
--- a/flang/include/flang/Runtime/iostat.h
+++ b/flang/include/flang/Runtime/iostat.h
@@ -67,6 +67,7 @@
   IostatMissingTerminator,
   IostatBadUnformattedRecord,
   IostatUTF8Decoding,
+  IostatUnitOverflow,
 };
 
 const char *IostatErrorString(int);
diff --git a/flang/runtime/io-api.cpp b/flang/runtime/io-api.cpp
--- a/flang/runtime/io-api.cpp
+++ b/flang/runtime/io-api.cpp
@@ -1275,4 +1275,51 @@
   IoStatementState &io{*cookie};
   return static_cast<enum Iostat>(io.EndIoStatement());
 }
+
+template <typename INT>
+static enum Iostat CheckUnitNumberInRangeImpl(INT unit, bool handleError,
+    char *ioMsg, std::size_t ioMsgLength, const char *sourceFile,
+    int sourceLine) {
+  if (unit != static_cast<ExternalUnit>(unit)) {
+    Terminator oom{sourceFile, sourceLine};
+    IoErrorHandler errorHandler{oom};
+    if (handleError) {
+      errorHandler.HasIoStat();
+      if (ioMsg) {
+        errorHandler.HasIoMsg();
+      }
+    }
+    if (static_cast<std::intmax_t>(unit) == unit) {
+      errorHandler.SignalError(IostatUnitOverflow,
+          "UNIT number %jd is out of range", static_cast<std::intmax_t>(unit));
+    } else {
+      // Avoid printing misleading info if SignalError cannot print the unit
+      // number accurately (when unit does not fit in a std::intmax_t).
+      errorHandler.SignalError(
+          IostatUnitOverflow, "UNIT number is out of range");
+    }
+    if (ioMsg) {
+      errorHandler.GetIoMsg(ioMsg, ioMsgLength);
+    }
+    return static_cast<enum Iostat>(errorHandler.GetIoStat());
+  }
+  return IostatOk;
+}
+
+enum Iostat IONAME(CheckUnitNumberInRange64)(std::int64_t unit,
+    bool handleError, char *ioMsg, std::size_t ioMsgLength,
+    const char *sourceFile, int sourceLine) {
+  return CheckUnitNumberInRangeImpl(
+      unit, handleError, ioMsg, ioMsgLength, sourceFile, sourceLine);
+}
+
+#ifdef __SIZEOF_INT128__
+enum Iostat IONAME(CheckUnitNumberInRange128)(common::int128_t unit,
+    bool handleError, char *ioMsg, std::size_t ioMsgLength,
+    const char *sourceFile, int sourceLine) {
+  return CheckUnitNumberInRangeImpl(
+      unit, handleError, ioMsg, ioMsgLength, sourceFile, sourceLine);
+}
+#endif
+
 } // namespace Fortran::runtime::io
diff --git a/flang/unittests/Runtime/ExternalIOTest.cpp b/flang/unittests/Runtime/ExternalIOTest.cpp
--- a/flang/unittests/Runtime/ExternalIOTest.cpp
+++ b/flang/unittests/Runtime/ExternalIOTest.cpp
@@ -895,3 +895,38 @@
   ASSERT_EQ(IONAME(EndIoStatement)(io), IostatOk)
       << "EndIoStatement() for second CLOSE";
 }
+
+TEST(ExternalIOTests, BigUnitNumbers) {
+  if (std::numeric_limits<ExternalUnit>::max() <
+      std::numeric_limits<std::int64_t>::max()) {
+    std::int64_t unit64Ok = std::numeric_limits<ExternalUnit>::max();
+    std::int64_t unit64Bad = unit64Ok + 1;
+    std::int64_t unit64Bad2 =
+        static_cast<std::int64_t>(std::numeric_limits<ExternalUnit>::min()) - 1;
+    EXPECT_EQ(IONAME(CheckUnitNumberInRange64)(unit64Ok, true), IostatOk);
+    EXPECT_EQ(IONAME(CheckUnitNumberInRange64)(unit64Ok, false), IostatOk);
+    EXPECT_EQ(
+        IONAME(CheckUnitNumberInRange64)(unit64Bad, true), IostatUnitOverflow);
+    EXPECT_EQ(
+        IONAME(CheckUnitNumberInRange64)(unit64Bad2, true), IostatUnitOverflow);
+    EXPECT_EQ(
+        IONAME(CheckUnitNumberInRange64)(unit64Bad, true), IostatUnitOverflow);
+    EXPECT_EQ(
+        IONAME(CheckUnitNumberInRange64)(unit64Bad2, true), IostatUnitOverflow);
+    constexpr std::size_t n{80};
+    char expectedMsg[n + 1];
+    expectedMsg[n] = '\0';
+    std::snprintf(expectedMsg, n, "UNIT number %jd is out of range",
+        static_cast<std::intmax_t>(unit64Bad));
+    EXPECT_DEATH(
+        IONAME(CheckUnitNumberInRange64)(2147483648, false), expectedMsg);
+    for (auto i{std::strlen(expectedMsg)}; i < n; ++i) {
+      expectedMsg[i] = ' ';
+    }
+    char msg[n + 1];
+    msg[n] = '\0';
+    EXPECT_EQ(IONAME(CheckUnitNumberInRange64)(unit64Bad, true, msg, n),
+        IostatUnitOverflow);
+    EXPECT_EQ(std::strncmp(msg, expectedMsg, n), 0);
+  }
+}