diff --git a/cwltool/context.py b/cwltool/context.py
index 83c098e1..daf6aa86 100644
--- a/cwltool/context.py
+++ b/cwltool/context.py
@@ -107,6 +107,7 @@ class RuntimeContext(ContextBase):
         self.pull_image = True  # type: bool
         self.rm_container = True  # type: bool
         self.move_outputs = "move"  # type: str
+        self.streaming_allowed: bool = False
 
         self.singularity = False  # type: bool
         self.debug = False  # type: bool
diff --git a/cwltool/job.py b/cwltool/job.py
index f515091e..0f9eb131 100644
--- a/cwltool/job.py
+++ b/cwltool/job.py
@@ -3,6 +3,7 @@ import functools
 import itertools
 import logging
 import os
+import stat
 import re
 import shutil
 import subprocess  # nosec
@@ -175,13 +176,24 @@ class JobBase(HasReqsHints, metaclass=ABCMeta):
         if not os.path.exists(self.outdir):
             os.makedirs(self.outdir)
 
+        def is_streamable(file: str) -> bool:
+            if not runtimeContext.streaming_allowed:
+                return False
+            for inp in self.joborder.values():
+                if isinstance(inp, dict) and inp.get("location", None) == file:
+                    return inp.get("streamable", False)
+            return False
+
         for knownfile in self.pathmapper.files():
             p = self.pathmapper.mapper(knownfile)
             if p.type == "File" and not os.path.isfile(p[0]) and p.staged:
-                raise WorkflowException(
-                    "Input file %s (at %s) not found or is not a regular "
-                    "file." % (knownfile, self.pathmapper.mapper(knownfile)[0])
-                )
+                if not (
+                    is_streamable(knownfile) and stat.S_ISFIFO(os.stat(p[0]).st_mode)
+                ):
+                    raise WorkflowException(
+                        "Input file %s (at %s) not found or is not a regular "
+                        "file." % (knownfile, self.pathmapper.mapper(knownfile)[0])
+                    )
 
         if "listing" in self.generatefiles:
             runtimeContext = runtimeContext.copy()

diff --git a/tests/test_streaming.py b/tests/test_streaming.py
new file mode 100644
index 00000000..e3d3ec75
--- /dev/null
+++ b/tests/test_streaming.py
@@ -0,0 +1,108 @@
+"""Test that files marked as 'streamable' when 'streaming_allowed' can be named pipes."""
+import os
+
+import pytest
+from pathlib import Path
+from typing import cast
+
+from ruamel.yaml.comments import CommentedMap
+from schema_salad.sourceline import cmap
+
+from cwltool.command_line_tool import CommandLineTool
+from cwltool.context import LoadingContext, RuntimeContext
+from cwltool.errors import WorkflowException
+from cwltool.job import JobBase
+from cwltool.update import INTERNAL_VERSION
+from cwltool.utils import CWLObjectType
+from .util import get_data
+
+toolpath_object = cast(
+    CommentedMap,
+    cmap(
+        {
+            "cwlVersion": INTERNAL_VERSION,
+            "class": "CommandLineTool",
+            "inputs": [
+                {
+                    "type": "File",
+                    "id": "inp",
+                    "streamable": True,
+                }
+            ],
+            "outputs": [],
+            "requirements": [],
+        }
+    ),
+)
+
+loading_context = LoadingContext(
+    {
+        "metadata": {
+            "cwlVersion": INTERNAL_VERSION,
+            "http://commonwl.org/cwltool#original_cwlVersion": INTERNAL_VERSION,
+        }
+    }
+)
+
+
+def test_regular_file() -> None:
+    """Test that regular files do not raise any exception when they are checked in job._setup."""
+    clt = CommandLineTool(
+        toolpath_object,
+        loading_context,
+    )
+    runtime_context = RuntimeContext()
+
+    joborder: CWLObjectType = {
+        "inp": {
+            "class": "File",
+            "location": get_data("tests/wf/whale.txt"),
+        }
+    }
+
+    job = next(clt.job(joborder, None, runtime_context))
+    assert isinstance(job, JobBase)
+
+    job._setup(runtime_context)
+
+
+streaming = [
+    (True, True, False),
+    (True, False, True),
+    (False, True, True),
+    (False, False, True),
+]
+
+
+@pytest.mark.parametrize("streamable,streaming_allowed,raise_exception", streaming)
+def test_input_can_be_named_pipe(
+    tmp_path: Path, streamable: bool, streaming_allowed: bool, raise_exception: bool
+) -> None:
+    """Test that input can be a named pipe."""
+    clt = CommandLineTool(
+        toolpath_object,
+        loading_context,
+    )
+
+    runtime_context = RuntimeContext()
+    runtime_context.streaming_allowed = streaming_allowed
+
+    path = tmp_path / "tmp"
+    os.mkfifo(path)
+
+    joborder: CWLObjectType = {
+        "inp": {
+            "class": "File",
+            "location": str(path),
+            "streamable": streamable,
+        }
+    }
+
+    job = next(clt.job(joborder, None, runtime_context))
+    assert isinstance(job, JobBase)
+
+    if raise_exception:
+        with pytest.raises(WorkflowException):
+            job._setup(runtime_context)
+    else:
+        job._setup(runtime_context)

Request for cwltool to support named pipes
## Expected Behavior
Some runners such as Toil might implement file streaming with named pipes when `streamable` flag is true:
https://github.com/DataBiosphere/toil/issues/3469

## Actual Behavior
An exception is raised because a named pipe is not a regular file:
https://github.com/common-workflow-language/cwltool/blob/ed9dd4c3472e940a52dfe90049895f470bfd7329/cwltool/job.py#L180

## Workflow Code
```
#!/usr/bin cwl-runner

cwlVersion: v1.2
class: CommandLineTool
baseCommand: cat

stdout: $(inputs.output_filename)
arguments: ["-A"]

inputs:
  input_file:
    type: File
    streamable: true
    inputBinding:
      position: 1
  output_filename:
    type: string?
    default: out.txt

outputs:
  count:
    type: stdout

```

## Your Environment
* cwltool version: 
3.0.20201203173111 (Linux)

tests/test_streaming.py::test_input_can_be_named_pipe[True-True-False]
tests/test_streaming.py::test_regular_file tests/test_streaming.py::test_input_can_be_named_pipe[True-False-True] tests/test_streaming.py::test_input_can_be_named_pipe[False-True-True] tests/test_streaming.py::test_input_can_be_named_pipe[False-False-True]