ACCORDING TO THE PILOT THE AIRCRAFT DEPARTED TUCSON, ARIZONA, ON THE MORNING OF JULY 31 FOR A FLIGHT TO YUCCA VALLEY. WHEN HE WAS READY TO DEPART ON THE RETURN LEG OF THE ROUND ROBIN CROSS COUNTRY THE PILOT DISCOVERED THAT NO FUEL SERVICE WAS AVAILABLE AT YUCCA VALLEY AND HE DEPARTED WITH THE INTENTION OF FUELING THE AIRCRAFT WHILE ENROUTE BACK TO TUCSON. AFTER DEPARTURE FROM YUCCA VALLEY, THE AIRCRAFT BY PASSED THE AIRPORTS AT PALM SPRINGS AND THERMAL, THEN OVER FLEW BLYTHE, CALIFORNIA. OVER BLYTHE THE PILOT SAID HE COULD NOT RAISE ANYONE ON THE UNICOM TO VERIFY IF FUEL WAS AVAILABLE. THE NEXT AIRPORT ON THE MOST DIRECT ROUTING TO TUCSON WAS GILA BEND, ARIZONA. THE AIRCRAFT WAS DESCENDING TOWARD THE GILA BEND AIRPORT WHEN THE ENGINE QUIT. THE AIRCRAFT LANDED SHORT OF THE RUNWAY IN A FIELD AND INCURRED SUBSTANTIAL DAMAGE. NO FUEL WAS FOUND IN THE AIRCRAFT FUEL TANKS.