Index: packages/Python/lldbsuite/test/functionalities/postmortem/elf-core/TestLinuxCore.py
===================================================================
--- packages/Python/lldbsuite/test/functionalities/postmortem/elf-core/TestLinuxCore.py
+++ packages/Python/lldbsuite/test/functionalities/postmortem/elf-core/TestLinuxCore.py
@@ -6,6 +6,7 @@
 
 import shutil
 import struct
+import os
 
 import lldb
 from lldbsuite.test.decorators import *
@@ -203,6 +204,33 @@
         for regname, value in values.iteritems():
             self.expect("register read {}".format(regname), substrs=["{} = {}".format(regname, value)])
 
+    @expectedFailureAll(bugnumber="llvm.org/pr37371", hostoslist=["windows"])
+    @skipIf(triple='^mips')
+    @skipIfLLVMTargetMissing("X86")
+    def test_i386_sysroot(self):
+        """Test that lldb can find the exe for an i386 linux core file using the sysroot."""
+
+        # Copy linux-i386.out to tmp_sysroot/home/labath/test/a.out (since it was compiled as
+        # /home/labath/test/a.out)
+        tmp_sysroot = "/tmp/lldb_i386_mock_sysroot"
+        executable = tmp_sysroot + "/home/labath/test/a.out"
+        lldbutil.mkdir_p(os.path.dirname(executable))
+        shutil.copyfile("linux-i386.out", executable)
+
+        # Set sysroot and load core
+        self.runCmd("platform select remote-linux --sysroot '%s'" % tmp_sysroot)
+        target = self.dbg.CreateTarget(None)
+        self.assertTrue(target, VALID_TARGET)
+        process = target.LoadCore("linux-i386.core")
+
+        # Check that we found a.out from the sysroot
+        self.check_all(process, self._i386_pid, self._i386_regions, "a.out")
+
+        self.dbg.DeleteTarget(target)
+
+        # Clean up tmp_sysroot
+        shutil.rmtree(tmp_sysroot)
+
     def check_memory_regions(self, process, region_count):
         region_list = process.GetMemoryRegions()
         self.assertEqual(region_list.GetSize(), region_count)
@@ -299,15 +327,7 @@
             self.dbg.SetOutputFileHandle(None, False)
             self.dbg.SetErrorFileHandle(None, False)
 
-    def do_test(self, filename, pid, region_count, thread_name):
-        target = self.dbg.CreateTarget(filename + ".out")
-        process = target.LoadCore(filename + ".core")
-        self.assertTrue(process, PROCESS_IS_VALID)
-        self.assertEqual(process.GetNumThreads(), 1)
-        self.assertEqual(process.GetProcessID(), pid)
-
-        self.check_state(process)
-
+    def check_stack(self, process, pid, thread_name):
         thread = process.GetSelectedThread()
         self.assertTrue(thread)
         self.assertEqual(thread.GetThreadID(), pid)
@@ -324,6 +344,21 @@
                 frame.FindVariable("F").GetValueAsUnsigned(), ord(
                     backtrace[i][0]))
 
+    def check_all(self, process, pid, region_count, thread_name):
+        self.assertTrue(process, PROCESS_IS_VALID)
+        self.assertEqual(process.GetNumThreads(), 1)
+        self.assertEqual(process.GetProcessID(), pid)
+
+        self.check_state(process)
+
+        self.check_stack(process, pid, thread_name)
+
         self.check_memory_regions(process, region_count)
 
+    def do_test(self, filename, pid, region_count, thread_name):
+        target = self.dbg.CreateTarget(filename + ".out")
+        process = target.LoadCore(filename + ".core")
+
+        self.check_all(process, pid, region_count, thread_name)
+
         self.dbg.DeleteTarget(target)
Index: source/Target/Platform.cpp
===================================================================
--- source/Target/Platform.cpp
+++ source/Target/Platform.cpp
@@ -228,17 +228,36 @@
         module_spec, module_sp, module_search_paths_ptr, old_module_sp_ptr,
         did_create_ptr, false);
 
+  // Module resolver lambda.
+  auto resolver = [&](const ModuleSpec &spec) {
+    Status error(eErrorTypeGeneric);
+    ModuleSpec resolved_spec;
+    // Check if we have sysroot set.
+    if (m_sdk_sysroot) {
+      // Prepend sysroot to module spec.
+      resolved_spec = spec;
+      resolved_spec.GetFileSpec().PrependPathComponent(
+        m_sdk_sysroot.GetStringRef());
+      // Try to get shared module with resolved spec.
+      error = ModuleList::GetSharedModule( 
+        resolved_spec, module_sp, module_search_paths_ptr, old_module_sp_ptr, 
+        did_create_ptr, false);
+    }
+    // If we don't have sysroot or it didn't work then 
+    // try original module spec.
+    if (!error.Success()) {
+      resolved_spec = spec;
+      error = ModuleList::GetSharedModule(
+        resolved_spec, module_sp, module_search_paths_ptr, old_module_sp_ptr, 
+        did_create_ptr, false);
+    }
+    if (error.Success() && module_sp)
+      module_sp->SetPlatformFileSpec(resolved_spec.GetFileSpec());
+    return error;
+  };
+
   return GetRemoteSharedModule(module_spec, process, module_sp,
-                               [&](const ModuleSpec &spec) {
-                                 Status error = ModuleList::GetSharedModule(
-                                     spec, module_sp, module_search_paths_ptr,
-                                     old_module_sp_ptr, did_create_ptr, false);
-                                 if (error.Success() && module_sp)
-                                   module_sp->SetPlatformFileSpec(
-                                       spec.GetFileSpec());
-                                 return error;
-                               },
-                               did_create_ptr);
+                               resolver, did_create_ptr);
 }
 
 bool Platform::GetModuleSpec(const FileSpec &module_file_spec,