diff --git a/fsliolib/CMakeLists.txt b/fsliolib/CMakeLists.txt
index 7ef4b63d..84bb69c5 100644
--- a/fsliolib/CMakeLists.txt
+++ b/fsliolib/CMakeLists.txt
@@ -16,3 +16,12 @@ if(BUILD_SHARED_LIBS)
   target_compile_definitions(${NIFTI_FSLIOLIB_NAME} PRIVATE NIFTI_FSL_BUILD_SHARED)
   target_compile_definitions(${NIFTI_FSLIOLIB_NAME} INTERFACE NIFTI_FSL_USE_SHARED)
 endif()
+
+if(NIFTI_BUILD_TESTING)
+  add_executable(${NIFTI_PACKAGE_PREFIX}fslio_volsize_test fslio_volsize_test.c)
+  target_link_libraries(${NIFTI_PACKAGE_PREFIX}fslio_volsize_test PUBLIC ${NIFTI_FSLIOLIB_NAME})
+  add_test(
+    NAME fslio_volsize_64bit
+    COMMAND $<TARGET_FILE:${NIFTI_PACKAGE_PREFIX}fslio_volsize_test>
+    )
+endif()
diff --git a/fsliolib/fslio.c b/fsliolib/fslio.c
index 44053fcf..6477d84e 100644
--- a/fsliolib/fslio.c
+++ b/fsliolib/fslio.c
@@ -918,7 +918,7 @@ size_t FslWriteVolumes(FSLIO *fslio, const void *buffer, size_t nvols)
     size_t bytes_written;
     size_t nbytes;
     long int bpv = fslio->niftiptr->nbyper;  /* bytes per voxel */
-    nbytes = nvols * FslGetVolSize(fslio) * bpv;
+    nbytes = nvols * FslGetVolSize(fslio) * (size_t)bpv;
 
     if ( (FslBaseFileType(FslGetFileType(fslio))==FSL_TYPE_ANALYZE)
          && (FslGetLeftRightOrder(fslio)==FSL_NEUROLOGICAL) ) {
@@ -1076,7 +1076,7 @@ size_t FslReadRowSeries(FSLIO *fslio, void *buffer, short row, short slice, size
     if ((slice<0) || (slice>=z)) FSLIOERR("FslReadRowSeries: slice outside valid range");
     if ((row<0) || (row>=y)) FSLIOERR("FslReadRowSeries: row outside valid range");
 
-    rowbytes = x * (FslGetDataType(fslio, &type)) / 8;
+    rowbytes = (size_t)x * (size_t)(FslGetDataType(fslio, &type)) / 8;
     slbytes = rowbytes * y;
     volbytes = slbytes * z;
 
@@ -1142,7 +1142,8 @@ size_t FslReadTimeSeries(FSLIO *fslio, void *buffer, short xVox, short yVox, sho
     volbytes = (size_t)xdim * (size_t)ydim * (size_t)zdim * wordsize;
 
     orig_offset = (size_t)znztell(fslio->fileptr);
-    offset = ((ydim * zVox + yVox) * xdim + xVox) * wordsize;
+    offset = (((size_t)ydim * (size_t)zVox + (size_t)yVox) * (size_t)xdim
+              + (size_t)xVox) * (size_t)wordsize;
     znzseek(fslio->fileptr,(znz_off_t)offset,SEEK_CUR);
 
     for (n=0; n<nvols; n++) {
@@ -1187,7 +1188,8 @@ size_t FslGetVolSize(FSLIO *fslio)
   /* returns number of voxels per 3D volume */
   if (fslio==NULL)  FSLIOERR("FslGetVolSize: Null pointer passed for FSLIO");
   if (fslio->niftiptr!=NULL) {
-    return (fslio->niftiptr->nx * fslio->niftiptr->ny * fslio->niftiptr->nz);
+    return (size_t)fslio->niftiptr->nx * (size_t)fslio->niftiptr->ny *
+           (size_t)fslio->niftiptr->nz;
   }
   if (fslio->mincptr!=NULL) {
     fprintf(stderr,"Warning:: Minc is not yet supported\n");
diff --git a/fsliolib/fslio_volsize_test.c b/fsliolib/fslio_volsize_test.c
new file mode 100644
index 00000000..9d25385b
--- /dev/null
+++ b/fsliolib/fslio_volsize_test.c
@@ -0,0 +1,42 @@
+/* FslGetVolSize() must evaluate nx*ny*nz at size_t width, not int width. */
+
+#include <stdio.h>
+#include <stdlib.h>
+#include "fslio.h"
+
+static int check(const char *what, size_t got, size_t want)
+{
+  if( got == want ) return 0;
+  fprintf(stderr, "FAILURE: %s: got %llu, expected %llu\n", what,
+          (unsigned long long)got, (unsigned long long)want);
+  return 1;
+}
+
+int main(void)
+{
+  FSLIO fslio;
+  nifti_image nim;
+  int failures = 0;
+
+  memset(&fslio, 0, sizeof(fslio));
+  memset(&nim, 0, sizeof(nim));
+  fslio.niftiptr = &nim;
+  fslio.mincptr = NULL;
+
+  nim.nx = 64; nim.ny = 64; nim.nz = 32;
+  failures += check("64x64x32", FslGetVolSize(&fslio), (size_t)64*64*32);
+
+  /* 2048*2048*1024 == 2^32: zero when the product is formed in int. */
+  nim.nx = 2048; nim.ny = 2048; nim.nz = 1024;
+  failures += check("2048x2048x1024", FslGetVolSize(&fslio),
+                    (size_t)2048*2048*1024);
+
+  /* 3000*3000*300 == 2,700,000,000: negative when formed in int. */
+  nim.nx = 3000; nim.ny = 3000; nim.nz = 300;
+  failures += check("3000x3000x300", FslGetVolSize(&fslio),
+                    (size_t)3000*3000*300);
+
+  if( failures ) return 1;
+  printf("FslGetVolSize 64-bit arithmetic test passed.\n");
+  return 0;
+}