A B737-300 INCURRED STRUCTURAL DAMAGE TO THE RADOME; LOWER SKIN AND BULKHEAD AT STATION 178; CAUSED BY IMPROPERLY CHOCKED ACFT ROLLING INTO A STORAGE CONTAINER.

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AT APPROX XA50; WE (EVENING SHOPS CREW) MOVED ACFT FROM HANGAR TO THE NEW WASH RACK. I WAS IN THE COCKPIT AS A BRAKE RIDER. AT THE COMPLETION OF THE TOW; I SET BRAKES AND SHUT DOWN THE ACFT; SECURED THE ACFT; COCKPIT AND DEPARTED. THE BRAKES BLED DOWN AT XB40. THE ACFT ROLLED INTO A BOX STRUCTURE. THE NOSE RADOME WAS DAMAGED AS WAS THE BULKHEAD AND LOWER SKIN. THE ACFT WAS CHOCKED AT THE NOSE TIRES ONLY. SUPPLEMENTAL INFO FROM ACN 605573: AFTER CHOCKING NOSE TIRES AND DISCONNECTING TUG AND TOWBAR; WE LEFT THE AREA. AFTER A FEW MINS; THE ACFT PUSHED THE CHOCK FORWARD AND THE NOSE GEAR TURNED TO THE L. IT ROLLED INTO A CONTAINER ABOUT 12 FT AWAY. THE RAMP IS SLOPED MORE THAN A CHOCK IN THE FRONT OF THE NOSE TIRE COULD HOLD. SUPPLEMENTAL INFO FROM ACN 605575: UPON ARR AT THE WASH RACK WE PULLED THE PLANE STRAIGHT; AND INTO THE CTR OF THE WASH RACK. I CHOCKED THE NOSEWHEELS; AND DISCONNECTED THE TOWBAR; AND TUG. I THEN LOOKED FOR A LADDER; TO GET THE BRAKE RIDER OUT OF THE COCKPIT -- I SAW ONE ON THE NEXT WASH RACK. I WALKED OVER TO THE NEXT WASH RACK; GOT THE LADDER; AND PUSHED IT BACK TO THE ACFT. WHILE PUSHING THE LADDER TO ACFT; I NOTICED THAT THE AFT CHOCK WAS ABOUT 4-6 INCHES BEHIND THE NOSEWHEEL. THEN I WENT DOWN TO THE NOSEWHEEL; AND MOVED THE AFT CHOCK; BACK; IN CONTACT; WITH THE NOSEWHEEL. A MECH CAME INTO THE BOOTH; AND SAID THE ACFT ON THE WASH RACK HAD ROLLED INTO THE STORAGE CONTAINER. WHEN I GOT TO THE WASH RACK; I SAW THAT THE ACFT HAD INDEED STRUCK THE STORAGE CONTAINER. I THEN PROCEEDED TO WHERE THE CHOCKS WERE; AND NOTICED MARKS ON THE CONCRETE THAT INDICATED THE NOSEWHEELS HAD TURNED L; APPROX 50 DEGS; AND PUSHED OUT OF THE CHOCKS. I BELIEVE THE CAUSE OF THIS EVENT WAS THE FAILURE OF THE WING WALKERS TO INSTALL MAIN TIRE CHOCKS; AND MY FAILURE TO REQUIRE THEM TO DO SO. I BELIEVE THE PROB IS SYSTEMIC IN THAT NO ONE; IN SHOPS; REQUIRES CHOCKS TO BE INSTALLED ON MAIN WHEELS. BY NO ONE; I AM REFERRING TO LEAD MEN; INSPECTORS; SAFETY; AND MGMNT.