A B737-300 FLYING IN ZME AIRSPACE FOLLOWS THE WRONG AIRWAY. FLT PLAN WAS NEVER CHKED AGAINST CLRNC RECEIVED.

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ACR FLT ABC DEPARTED JACKSON; MS; ENRTE TO MDW. LEVEL CRUISE FLT. HAD THE AUTOPLT FLYING LNAV ROUTING THAT SHOWED MEM J29 PXV; WHEN OUR ACTUAL ROUTING FROM OUR DISPATCH (AND THE RTE GIVEN TO US BY CLRNC DELIVERY IN JAN) WAS MEM J35 FAM. AUTOPLT JOINED J29 AND SHORTLY THEREAFTER THE ZME CTLR ADVISED US WE WERE SUPPOSED TO BE ON J35. WE TURNED L TO JOIN THE AIRWAY; REPROGRAMMED THE CDU FOR PROPER ROUTING AND CONTINUED TO DEST. NO TFC CONFLICTS WERE ADVISED BY ZME; AND NONE ON TCASII. I SHOULD HAVE STUDIED THE COMPLETE RTE IN THE CDU AND COMPARED WITH THE FILED ROUTING. SUPPLEMENTAL INFO FROM ACN 392524: FLT FROM JACKSON; MS; TO MDW; IL. FLT PLAN FILED BY COMPANY DISPATCH (JAN DIRECT SQS J35 CAPITAL.MOTIF ARR) DIFFERED FROM STANDARD COMPANY RTE STORED IN ACFT FMS (JAN DIRECT SQS J35 MEM J29 PXV DIRECT TTH DIRECT BVT.BVT2 ARR). CAPT WAS FLYING; AUTOPLT ENGAGED; LNAV MODE SELECTED. I (FO) WAS 'BACKING UP' NAV ON VOR (J35 COURSE INBOUND TO MEM). JUST PRIOR TO MEM; FLT ATTENDANT CAME IN COCKPIT TO TAKE COFFEE ORDERS. SHE RETURNED WITH COFFEE; STARTED ASKING ABOUT COMPANY'S HIRING REQUIREMENTS; AS HER BROTHER IS WANTING TO APPLY. ACFT MAKES SLIGHT R TURN TO INTERCEPT J29 OVER MEM (INSTEAD OF STAYING ON J35; AS FILED). APPROX 10 DME N OF MEM; CTR CTLR ASKS IF WE'RE TURNING TO INTERCEPT J35; SHOWS US E OF COURSE. CAPT REALIZES WRONG TURN BY FMS/LNAV. HE SELECTS HDG MODE; TURNS FOR J35 INTERCEPT. SOON AFTER; CTLR GIVES US FREQ CHANGE. NEW CTLR GIVES US DIRECT CAP. REST OF FLT UNEVENTFUL. CONTRIBUTING FACTORS: DISTR BY FLT ATTENDANT'S SVC; QUESTIONS DURING APCH TO AND OVERFLT OF MEM VOR. HAD ARRIVED EARLY AT JAN ON PREVIOUS LEG. HAD NOT RECEIVED RELEASE WITH DISPATCH FILED FLT PLAN INFO YET WHEN FMS LOADED WITH CANNED COMPANY RTE. DIDN'T HAVE IT TO COMPARE THE TWO. SHOULD HAVE COMPARED PRIOR TO PUSHBACK ONCE RELEASE PAPERWORK WAS BROUGHT TO COCKPIT.