FLC OF B727 DURING TAXI HAS R MAIN GEAR EXIT THE TXWY AND BECOME MIRED IN THE GRASS AND MUD. PAX DEPLANED AND ACFT TOWED OUT.

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OUR FLT WAS SCHEDULED FROM TYS TO ATL. WE WERE CLRED TO TAXI TO RWY 23L. WE WERE ON TXWY A APCHING THE DEP END OF RWY 23L. THERE WAS A LIGHT CIVIL ACFT ON TXWY A9. TWR ASKED IF WE COULD GET AROUND THAT ACFT. WE REPLIED NEGATIVE. TWR THEN CLRED US TO USE TXWY A8 AND BACK TAXI TO THE END OF RWY 23L. I MADE A L TURN ONTO TXWY A8 FOLLOWED BY A R TURN ONTO RWY 23L. AT APPROX 60 DEGS THROUGH THIS TURN WE FELT THE ACFT SHUDDER SLIGHTLY AND COME TO A STOP AND LEANING SLIGHTLY TO THE R. WE ASKED TWR IF OUR R MAIN GEAR HAD GONE OFF THE TXWY. THEY SAID THAT IT APPEARED TO THEM IT HAD. WE CALLED THE RAMP FOR A TUG. WE INFORMED OUR PAX OF WHAT HAD HAPPENED AND THEN CALLED OUR DISPATCHER IN ATL VIA RADIO. WHEN THE TUG AND GND CREW ARRIVED THEY CONFIRMED THAT OUR R MAIN GEAR HAD GONE IN THE GRASS APPROX 3 FT FROM THE EDGE OF THE TXWY AT THE CORNER OF TXWY A8 AND RWY 23L. THE INITIAL TIRE DEPTH IN THE GRASS WAS APPROX 6 INCHES. AS WE GATHERED MORE INFO FROM OUR GND CREW ON THE CONDITION OF OUR R GEAR; IT WAS NOTED THAT THE TIRES WERE SLOWLY SINKING IN THE GRASS AND MUD UNDERNEATH. IT BECAME APPARENT THAT WE WOULD NOT ATTEMPT TO PWR OUT OR USE THE TUG. THE TIRE ENDED UP SINKING ANOTHER 3-4 INCHES ACCORDING TO OUR GND CREW. THROUGHOUT THIS WHOLE EVENT; WE WERE IN RADIO CONTACT WITH OUR DISPATCHER AND OUR MAINT COORDINATOR. WE ALL AGREED THAT THE SAFEST COURSE OF ACTION WOULD BE TO DEPLANE OUR PAX AND UNLOAD OUR CARGO. THIS WAS ACCOMPLISHED WHEN THE BUSES ARRIVED TO TAKE OUR PAX TO THE TERMINAL. ANOTHER ACFT WAS DISPATCHED FROM ATL TO ACCOMMODATE OUR PAX; ALONG WITH A MAINT TEAM TO INSPECT THE ACFT. THE MAINT TEAM INSPECTED THE ACFT AND FOUND NO DAMAGE. THEY PLACED STEEL PLATES IN FRONT OF THE R TIRES AND TOWED THE ACFT BACK ONTO THE HARD SURFACE. WE HAD NO INJURIES OR ACFT DAMAGED. LESSONS LEARNED: ALTHOUGH I HAVE OVER 5000 HRS IN THE B727; I HAVE ONLY 85 HRS IN THE L SEAT AS A NEW CAPT. ALL OF MY FORMER TAXIING EXPERIENCE HAS BEEN ON FIGHTER SIZE ACFT. MY PLAN WAS TO BACK TAXI DOWN ON THE COPLT'S SIDE OF THE RWY AND MAKE THE 180 DEG TURN TO THE L. I MISJUDGED THE TURN FROM THE TXWY ONTO THE RWY; RESULTING IN THE R MAIN GEAR GOING OFF THE EDGE OF THE HARD SURFACE. I THINK IT IS ALSO IMPORTANT TO NOTE THAT; EMBARRASSING AS IT IS TO BE IN A HOLE; IT IS BEST NOT TO DIG THAT HOLE DEEPER BY TRYING TO PWR OUT OR PULL THE ACFT OUT WITH PAX ON BOARD. THAT RISKS INJURY OR ACFT DAMAGE. PREVENTIVE RECOMMENDATIONS: I THINK ADDING MORE EMPHASIS ON TIPS FOR TAXIING THE ACFT TO OUR TRAINING PROGRAM AND ON OUR IOE WITH OUR LINE CHK AIRMAN; WHO HELP NEW CAPTS. THIS COULD INCLUDE THESE SITS OF MAKING SHORT RADIUS TURNS AND 180S; THAT WE NORMALLY DON'T SEE UNTIL WE NEED TO DO THEM.