diff --git a/buildstream/sandbox/_sandboxbwrap.py b/buildstream/sandbox/_sandboxbwrap.py
index 2352843..2bcb80b 100644
--- a/buildstream/sandbox/_sandboxbwrap.py
+++ b/buildstream/sandbox/_sandboxbwrap.py
@@ -49,6 +49,14 @@
         '/dev/zero'
     ]
 
+    ARCHITECTURES = {
+        'amd64': 'x86_64',
+        'arm64': 'aarch64',
+        'i386': 'i686',
+        'armhf': 'armv7l',
+        'ppc64el': 'ppc64le',
+    }
+
     def __init__(self, *args, **kwargs):
         super().__init__(*args, **kwargs)
         self.user_ns_available = kwargs['user_ns_available']
@@ -58,11 +66,25 @@
         host_os, _, _, _, host_arch = os.uname()
         config = self._get_config()
 
-        # We can't do builds for another host or architecture except 32 bit on 64 bit
+        # We can't do builds for another host OS
         if config.build_os != host_os:
             raise SandboxError("Configured and host OS don't match.")
 
         if config.build_arch != host_arch:
+            try:
+                archtest = utils.get_host_tool('arch-test')
+                supported = subprocess.getoutput(archtest).splitlines()
+                supported_architectures = map(self.ARCHITECTURES.get, supported, supported)
+            except utils.ProgramNotFoundError:
+                supported_architectures = []
+                if host_arch == "x86_64":
+                    supported_architectures = ["i686"]
+                elif host_arch == "aarch64":
+                    supported_architectures = ["armv7l"]
+
+            if config.build_arch not in supported_architectures:
+                raise SandboxError("Configured and host architecture don't match.")
+
             if ((config.build_arch == "i686" and host_arch == "x86_64") or
                 (config.build_arch == "armv7l" and host_arch == "aarch64")):
                 # check whether linux32 is available
@@ -71,8 +93,6 @@
                     self._linux32 = True
                 except utils.ProgramNotFoundError as e:
                     raise SandboxError("Configured and host architecture don't match.") from e
-            else:
-                raise SandboxError("Configured and host architecture don't match.")
 
     def run(self, command, flags, *, cwd=None, env=None):
         stdout, stderr = self._get_output()