diff --git a/gdb/ChangeLog b/gdb/ChangeLog
index 3a730c8..cca1af9 100644
--- a/gdb/ChangeLog
+++ b/gdb/ChangeLog
@@ -1,3 +1,9 @@
+2017-12-14  Joel Brobecker  <brobecker@adacore.com>
+
+	* ada-tasks.c (read_atcb): Properly set task_info->ptid
+	when !target_has_execution as well.
+	(task_command): Remove error when !target_has_execution.
+
 2017-12-13  Simon Marchi  <simon.marchi@ericsson.com>
 
 	* location.h (string_to_event_location): Add match_type
diff --git a/gdb/ada-tasks.c b/gdb/ada-tasks.c
index eac6c5b..cd324b7 100644
--- a/gdb/ada-tasks.c
+++ b/gdb/ada-tasks.c
@@ -783,18 +783,10 @@ read_atcb (CORE_ADDR task_id, struct ada_task_info *task_info)
     = value_as_long (value_field (common_value,
 				  pspace_data->atcb_fieldno.base_cpu));
 
-  /* And finally, compute the task ptid.  Note that there are situations
-     where this cannot be determined:
-       - The task is no longer alive - the ptid is irrelevant;
-       - We are debugging a core file - the thread is not always
-         completely preserved for us to link back a task to its
-         underlying thread.  Since we do not support task switching
-         when debugging core files anyway, we don't need to compute
-         that task ptid.
-     In either case, we don't need that ptid, and it is just good enough
-     to set it to null_ptid.  */
-
-  if (target_has_execution && ada_task_is_alive (task_info))
+  /* And finally, compute the task ptid.  Note that there is not point
+     in computing it if the task is no longer alive, in which case
+     it is good enough to set its ptid to the null_ptid.  */
+  if (ada_task_is_alive (task_info))
     task_info->ptid = ptid_from_atcb_common (common_value);
   else
     task_info->ptid = null_ptid;
@@ -1366,23 +1358,7 @@ task_command (const char *taskno_str, int from_tty)
   if (taskno_str == NULL || taskno_str[0] == '\0')
     display_current_task_id ();
   else
-    {
-      /* Task switching in core files doesn't work, either because:
-           1. Thread support is not implemented with core files
-           2. Thread support is implemented, but the thread IDs created
-              after having read the core file are not the same as the ones
-              that were used during the program life, before the crash.
-              As a consequence, there is no longer a way for the debugger
-              to find the associated thead ID of any given Ada task.
-         So, instead of attempting a task switch without giving the user
-         any clue as to what might have happened, just error-out with
-         a message explaining that this feature is not supported.  */
-      if (!target_has_execution)
-        error (_("\
-Task switching not supported when debugging from core files\n\
-(use thread support instead)"));
-      task_command_1 (taskno_str, from_tty, current_inferior ());
-    }
+    task_command_1 (taskno_str, from_tty, current_inferior ());
 }
 
 /* Indicate that the given inferior's task list may have changed,
diff --git a/gdb/testsuite/ChangeLog b/gdb/testsuite/ChangeLog
index 5dc7fc2..53c3780 100644
--- a/gdb/testsuite/ChangeLog
+++ b/gdb/testsuite/ChangeLog
@@ -1,3 +1,7 @@
+2017-12-14  Joel Brobecker  <brobecker@adacore.com>
+
+	* gdb.ada/task_switch_in_core: New testcase.
+
 2017-12-13  Simon Marchi  <simon.marchi@ericsson.com>
 
 	* gdb.python/py-breakpoint.c (foo_ns::multiply): New function.
diff --git a/gdb/testsuite/gdb.ada/task_switch_in_core.exp b/gdb/testsuite/gdb.ada/task_switch_in_core.exp
new file mode 100644
index 0000000..92e749f
--- /dev/null
+++ b/gdb/testsuite/gdb.ada/task_switch_in_core.exp
@@ -0,0 +1,80 @@
+# Copyright 2017 Free Software Foundation, Inc.
+
+# This program is free software; you can redistribute it and/or modify
+# it under the terms of the GNU General Public License as published by
+# the Free Software Foundation; either version 3 of the License, or
+# (at your option) any later version.
+#
+# This program is distributed in the hope that it will be useful,
+# but WITHOUT ANY WARRANTY; without even the implied warranty of
+# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+# GNU General Public License for more details.
+#
+# You should have received a copy of the GNU General Public License
+# along with this program.  If not, see <http://www.gnu.org/licenses/>.
+
+load_lib "ada.exp"
+
+standard_ada_testfile crash
+
+if {[gdb_compile_ada "${srcfile}" "${binfile}" executable [list debug]] != "" } {
+  return -1
+}
+
+clean_restart ${testfile}
+
+# Run the program to a certain point, and then use the gcore command
+# to generate a core file. The only objective of this part of this
+# testcase is to generate this core file, so we can then exercise
+# task-switching when debugging from core files.
+
+if { ![runto request_for_crash ]} then {
+    untested "couldn't run to Request_For_Crash"
+    return -1
+}
+
+set corefile [standard_output_file crash.gcore]
+set core_supported [gdb_gcore_cmd "$corefile" "save a corefile"]
+if {!$core_supported} {
+  return -1
+}
+
+# Now taht the core file has been created, we can start the real
+# part of this testcase, which is to debug using that core file.
+# Restart GDB and load that core file.
+
+clean_restart ${testfile}
+
+set core_loaded [gdb_core_cmd "$corefile" "re-load generated corefile"]
+if { $core_loaded == -1 } {
+    # No use proceeding from here.
+    return
+}
+
+# First, switch to task 1.
+
+gdb_test "task 1" \
+         "crash\\.request_for_crash \\(\\) at .*crash\\.adb:$decimal.*"
+
+
+gdb_test "info tasks" \
+         [multi_line "\\s+ID\\s+TID\\s+P-ID\\s+Pri\\s+State\\s+Name" \
+                     "\\*\\s+1\\s+.*main_task" \
+                     "\\s+2.*my_t"] \
+         "info tasks after switching to task 1"
+
+# Switch to task 2. Unlike in the case where we tested the switch to
+# task 1, don't check the location where the debugger says the program
+# is, as this might depend on the runtime, and in particular it might
+# depend on whether the runtime is built with debugging information
+# or not. Just check that we get the "switching to task" message, and
+# we will verify right after with an additional test that the current
+# task is now task 2.
+gdb_test "task 2" \
+         "\\\[Switching to task 2\\\].*"
+
+gdb_test "info tasks" \
+         [multi_line "\\s+ID\\s+TID\\s+P-ID\\s+Pri\\s+State\\s+Name" \
+                     "\\s+1\\s+.*main_task" \
+                     "\\*\\s+2.*my_t"] \
+         "info tasks after switching to task 2"
diff --git a/gdb/testsuite/gdb.ada/task_switch_in_core/crash.adb b/gdb/testsuite/gdb.ada/task_switch_in_core/crash.adb
new file mode 100644
index 0000000..ae0170d
--- /dev/null
+++ b/gdb/testsuite/gdb.ada/task_switch_in_core/crash.adb
@@ -0,0 +1,53 @@
+--  Copyright 2017 Free Software Foundation, Inc.
+--
+--  This program is free software; you can redistribute it and/or modify
+--  it under the terms of the GNU General Public License as published by
+--  the Free Software Foundation; either version 3 of the License, or
+--  (at your option) any later version.
+--
+--  This program is distributed in the hope that it will be useful,
+--  but WITHOUT ANY WARRANTY; without even the implied warranty of
+--  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+--  GNU General Public License for more details.
+--
+--  You should have received a copy of the GNU General Public License
+--  along with this program.  If not, see <http://www.gnu.org/licenses/>.
+
+with Ada.Text_IO; use Ada.Text_IO;
+
+procedure Crash is
+
+   procedure Request_For_Crash is
+   begin
+      null; -- Just an anchor for the debugger...
+   end Request_For_Crash;
+
+   task type T is
+      entry Done;
+   end T;
+
+   task body T is
+   begin
+      accept Done do
+         null;
+      end Done;
+      Put_Line ("Task T: Rendez-vous completed.");
+   end T;
+
+   My_T : T;
+
+begin
+
+   --  Give some time for the task to be created, and start its execution,
+   --  so that it reaches the accept statement.
+   delay 0.01;
+
+   Request_For_Crash;
+
+   delay 0.01;
+   Put_Line ("*** We didn't crash !?!");
+
+   --  Complete the rendez-vous with our task, so it can complete.
+   My_T.Done;
+
+end Crash;
