diff --git a/build/pkgs/flint/checksums.ini b/build/pkgs/flint/checksums.ini
index 53a1842d271..2e6af858963 100644
--- a/build/pkgs/flint/checksums.ini
+++ b/build/pkgs/flint/checksums.ini
@@ -1,4 +1,4 @@
 tarball=flint-VERSION.tar.gz
-sha1=dae6d32b25e46a6ab92514b4dfa64b06fdf247ec
-sha256=64d70e513076cfa971e0410b58c1da5d35112913e9a56b44e2c681b459d3eafb
+sha1=50d6c95ed5a601cd1b5b149ec42a84a54d58c2bd
+sha256=9497679804dead926e3affeb8d4c58739d1c7684d60c2c12827550d28e454a33
 upstream_url=https://github.com/flintlib/flint/releases/download/vVERSION/flint-VERSION.tar.gz
diff --git a/build/pkgs/flint/package-version.txt b/build/pkgs/flint/package-version.txt
index bea438e9ade..18091983f59 100644
--- a/build/pkgs/flint/package-version.txt
+++ b/build/pkgs/flint/package-version.txt
@@ -1 +1 @@
-3.3.1
+3.4.0
diff --git a/build/pkgs/flint/spkg-configure.m4 b/build/pkgs/flint/spkg-configure.m4
index d6d21b80fae..41418bfc0a1 100644
--- a/build/pkgs/flint/spkg-configure.m4
+++ b/build/pkgs/flint/spkg-configure.m4
@@ -3,12 +3,12 @@ SAGE_SPKG_CONFIGURE([flint], [
         AC_CHECK_HEADERS([flint/flint.h flint/padic.h], [dnl
           dnl gr_get_fexpr appears in Flint 3.0
           AC_SEARCH_LIBS([gr_get_fexpr], [flint], [dnl
-            dnl Assume Flint 3.4 is too new
-            AC_MSG_CHECKING([whether FLINT version is >= 3.4.0])
+            dnl Assume Flint 3.5 is too new
+            AC_MSG_CHECKING([whether FLINT version is >= 3.5.0])
             AC_COMPILE_IFELSE([dnl
               AC_LANG_PROGRAM([[#include <flint/flint.h>
-                                #if __FLINT_RELEASE > 30399
-                                # error "FLINT 3.4 is too new"
+                                #if __FLINT_RELEASE > 30499
+                                # error "FLINT 3.5 is too new"
                                 #endif
                               ]])
             ], [dnl