CARGO ACFT RAMP CHKED WHEN PARKED. FAA FINDS A CUT IN TIRE.

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FLT JFK TO ATL. UPON ARR AT ATLANTA HARTSFIELD I SECURED THE ACFT MYSELF. THE CAPT FO HAD ALREADY GONE INSIDE THE CARGO BUILDING. I SUPERVISED THE UNLOADING OF FREIGHT. THE RAMP HANDLERS SEEMED TO TAKE LONGER THAN USUAL (NOT OUR OWN PEOPLE). I WRAPPED UP EVERYTHING IN THE COCKPIT BUT THE 'B' PUMPS; THE APU AND THE BATTERY. I HAD AMPLE TIME; SO I DID A WALK AROUND -- NOT AS THOROUGH AS I WOULD HAVE DONE ON ACFT ACCEPTANCE PRIOR TO FLT. I LEFT THE AIR STAIR DOWN BECAUSE I DID NOT KNOW IF THE RAMP PEOPLE WOULD WANT TO PUT THE TAILSTAND BACK IN THE ACFT; AND THE AIR STAIR ALSO ACTS AS A TAILSTAND WHEN LOADING/UNLOADING OUR LGT. I CONTINUED MY WALK AROUND AND NOTED NO DISCREPANCIES AT ALL. I BUTTONED UP THE COCKPIT (CARGO DOOR; 'B' PUMPS; APU BATTERY) AND CLOSED THE SIDE DOOR (MAIN ENTRANCE). AFTER THE EQUIP WAS MOVED AWAY FROM THE ACFT; I RAISED THE AIR STAIR. SEVERAL HRS LATER THE FAA RAMPED OUR AIRPLANE AND NOTED A CUT IN THE #3 MAIN TIRE. THE TIRE WAS BEING CHANGED THAT EVENING WHEN WE ARRIVED TO FLY BACK TO JFK. ABOUT 1 WK LATER MY SUPVR WANTED ME TO EXPLAIN WHY THE TIRE WAS NOT CAUGHT ON MY 'POST FLT' -- THE FAA WAS ASKING... THERE ARE SEVERAL REASONS: THE WX WAS POOR AND IT HAD BEEN RAINING. THE TIRES MAY HAVE BEEN WET; MAKING TIRE CRACKS LOOK BETTER THAN THEY MAY BE. MOST PLTS RUSH AWAY FROM THE AIRPLANE; LEAVING THE SO BEHIND. A PRUDENT SO DOING A POST FLT IS VERY RUSHED; AND WOULD MOST LIKELY BE LEFT BEHIND WHEN THE HOTEL VAN SHOWS UP. NEITHER OUR GENERAL OPS MANUAL OR OUR ACFT OPS MANUAL REQUIRE THE SO TO DO A POST FLT ON TERMINATION (WHICH THIS WAS). I AM TOLD THAT SO'S ARE INSTRUCTED TO DO SO IN IOE... I WAS NOT. I HAVE A COPY OF OUR COMPANY TRAINING MANUAL. IT DOES NOT OUTLINE ANY POST FLT IN IOE. MOST PLTS LOCK THE ACFT WALK AWAY -- LEAVING THIS TYPE OF PROBLEM FOR PREFLT WHICH IS WHERE I WOULD HAVE CAUGHT IT.