diff --git a/docs/changes.txt b/docs/changes.txt
index 2b982c304a..5ac1eb417a 100644
--- a/docs/changes.txt
+++ b/docs/changes.txt
@@ -106,6 +106,7 @@ All:
 - Add UTF-8 support to wxZipOutputStream (Tobias Taschner).
 - Update all bundled 3rd party libraries to their latest versions.
 - Use unique prefix for all zlib symbols to avoid link conflicts.
+- Make wxFile::ReadAll() work for unseekable files too.
 
 All (GUI):
 
diff --git a/interface/wx/file.h b/interface/wx/file.h
index 31ea6bdd4f..78fb12aa3c 100644
--- a/interface/wx/file.h
+++ b/interface/wx/file.h
@@ -377,6 +377,8 @@ public:
     /**
         Reads the entire contents of the file into a string.
 
+        Since wxWidgets 3.1.1 this method also works for unseekable files.
+
         @param str
             Non-@NULL pointer to a string to read data into.
         @param conv
diff --git a/src/common/file.cpp b/src/common/file.cpp
index 0e976273dc..84cf9f78fc 100644
--- a/src/common/file.cpp
+++ b/src/common/file.cpp
@@ -261,24 +261,71 @@ bool wxFile::ReadAll(wxString *str, const wxMBConv& conv)
 {
     wxCHECK_MSG( str, false, wxS("Output string must be non-NULL") );
 
+    static const ssize_t READSIZE = 4096;
+
+    wxCharBuffer buf;
+
     ssize_t length = Length();
-    wxCHECK_MSG( (wxFileOffset)length == Length(), false, wxT("huge file not supported") );
-
-    wxCharBuffer buf(length);
-    char* p = buf.data();
-    for ( ;; )
+    if ( length != -1 )
     {
-        static const ssize_t READSIZE = 4096;
+        wxCHECK_MSG( (wxFileOffset)length == Length(), false, wxT("huge file not supported") );
 
-        ssize_t nread = Read(p, length > READSIZE ? READSIZE : length);
-        if ( nread == wxInvalidOffset )
+        if ( !buf.extend(length) )
             return false;
 
-        p += nread;
-        if ( length <= nread )
-            break;
+        char* p = buf.data();
+        for ( ;; )
+        {
+            ssize_t nread = Read(p, length > READSIZE ? READSIZE : length);
+            if ( nread == wxInvalidOffset )
+                return false;
 
-        length -= nread;
+            if ( nread == 0 )
+            {
+                // We have reached EOF before reading the entire length of the
+                // file. This can happen for some special files (e.g. those
+                // under /sys on Linux systems) or even for regular files if
+                // another process has truncated the file since we started
+                // reading it, so deal with it gracefully.
+                buf.shrink(p - buf.data());
+                break;
+            }
+
+            p += nread;
+            length -= nread;
+
+            if ( !length )
+            {
+                // Notice that we don't keep reading after getting the expected
+                // number of bytes, even though in principle a situation
+                // similar to the one described above, with another process
+                // extending the file since we started to read it, is possible.
+                // But returning just the data that was in the file when we
+                // originally started reading it isn't really wrong in this
+                // case, so keep things simple and just do it like this.
+                break;
+            }
+        }
+    }
+    else // File is not seekable
+    {
+        for ( ;; )
+        {
+            const size_t len = buf.length();
+            if ( !buf.extend(len + READSIZE) )
+                return false;
+
+            ssize_t nread = Read(buf.data() + len, READSIZE);
+            if ( nread == wxInvalidOffset )
+                return false;
+
+            if ( nread < READSIZE )
+            {
+                // We have reached EOF.
+                buf.shrink(len + nread);
+                break;
+            }
+        }
     }
 
     str->assign(buf, conv);
diff --git a/tests/file/filetest.cpp b/tests/file/filetest.cpp
index fdad2d8e4a..faeed69dbf 100644
--- a/tests/file/filetest.cpp
+++ b/tests/file/filetest.cpp
@@ -139,4 +139,28 @@ void FileTestCase::TempFile()
     CPPUNIT_ASSERT( wxRemoveFile(wxT("test2")) );
 }
 
+#ifdef __LINUX__
+
+// Check that GetSize() works correctly for special files.
+TEST_CASE("wxFile::Special", "[file][linux][special-file]")
+{
+    // This file is not seekable and has 0 size, but can still be read.
+    wxFile fileProc("/proc/diskstats");
+    CHECK( fileProc.IsOpened() );
+
+    wxString s;
+    CHECK( fileProc.ReadAll(&s) );
+    CHECK( !s.empty() );
+
+    // All files in /sys seem to have size of 4KiB currently, even if they
+    // don't have that much data in them.
+    wxFile fileSys("/sys/power/state");
+    CHECK( fileSys.IsOpened() );
+    CHECK( fileSys.ReadAll(&s) );
+    CHECK( !s.empty() );
+    CHECK( s.length() < 4096 );
+}
+
+#endif // __LINUX__
+
 #endif // wxUSE_FILE