diff --git a/Misc/NEWS.d/next/Build/2020-12-20-02-35-28.bpo-42604.gRd89w.rst b/Misc/NEWS.d/next/Build/2020-12-20-02-35-28.bpo-42604.gRd89w.rst
new file mode 100644
index 00000000000000..caaada41cf9bad
--- /dev/null
+++ b/Misc/NEWS.d/next/Build/2020-12-20-02-35-28.bpo-42604.gRd89w.rst
@@ -0,0 +1,4 @@
+Now all platforms use a value for the "EXT_SUFFIX" build variable derived
+from SOABI (for instance in freeBSD, "EXT_SUFFIX" is now ".cpython-310d.so"
+instead of ".so"). Previosuly only Linux, Mac and VxWorks were using a value
+for "EXT_SUFFIX" that included "SOABI".
diff --git a/configure b/configure
index ed969c55b35ab6..1252335472f561 100755
--- a/configure
+++ b/configure
@@ -15382,13 +15382,7 @@ _ACEOF
 
 fi
 
-
-case $ac_sys_system in
-    Linux*|GNU*|Darwin|VxWorks)
-	EXT_SUFFIX=.${SOABI}${SHLIB_SUFFIX};;
-    *)
-	EXT_SUFFIX=${SHLIB_SUFFIX};;
-esac
+EXT_SUFFIX=.${SOABI}${SHLIB_SUFFIX}
 
 { $as_echo "$as_me:${as_lineno-$LINENO}: checking LDVERSION" >&5
 $as_echo_n "checking LDVERSION... " >&6; }
diff --git a/configure.ac b/configure.ac
index c74e348e077fb7..972287a9c47661 100644
--- a/configure.ac
+++ b/configure.ac
@@ -4783,12 +4783,7 @@ if test "$Py_DEBUG" = 'true' -a "$with_trace_refs" != "yes"; then
 fi
 
 AC_SUBST(EXT_SUFFIX)
-case $ac_sys_system in
-    Linux*|GNU*|Darwin|VxWorks)
-	EXT_SUFFIX=.${SOABI}${SHLIB_SUFFIX};;
-    *)
-	EXT_SUFFIX=${SHLIB_SUFFIX};;
-esac
+EXT_SUFFIX=.${SOABI}${SHLIB_SUFFIX}
 
 AC_MSG_CHECKING(LDVERSION)
 LDVERSION='$(VERSION)$(ABIFLAGS)'