GPWS ALARM ACTIVATED AS ACFT IS VECTORED FOR APCH INTO DEN.

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ON THE APCH TO RWY 35R AT DEN WE WERE BEING VECTORED S OF THE FIELD AND W OF THE FINAL APCH COURSE. SOME DISTANCE JUST S OF ENGLE AT 9000 FT MSL AND IN HVY RAINSTORMS WITH LIGHTNING AND LIGHT CHOP WE WERE TURNED TO A BASE LEG. SHORTLY AFTER TURNING WE RECEIVED A GPWS WARNING 'TERRAIN; TERRAIN.' I DISCONNECTED THE AUTOPLT AND BEGAN A CLB CONTINUING THE TURN TO TRY TO GET US OUT OF THE WX. DURING THIS MANEUVER THE GPWS CONTINUED TO GO OFF ALMOST CONTINUOUSLY WITH 'TERRAIN; TERRAIN' OR 'PULL UP;' OR 'TOO LOW; TERRAIN.' ALSO; THE TURN DIVERGED US SIGNIFICANTLY FROM THE FINAL APCH COURSE. CONFIGN WAS 170 KTS WITH FLAPS AT 1 DEG. CLB THEREFORE WAS SOMEWHAT SLOW. APCH CTL QUERIED US ON 'WHERE WE WERE GOING' AND PNF EXPLAINED OUR TERRAIN WARNING. THE WARNINGS FINALLY CEASED AS WE LEVELED AT 10000 FT AND RETURNED TO THE FINAL APCH COURSE FOR UNEVENTFUL LNDG. ANY AND ALL DEVS FROM ATC CLRNCS WERE DUE ENTIRELY TO CONTINUOUS TERRAIN WARNINGS IN IMC. AREA WX WAS NUMEROUS TSTMS SURROUNDING THE FIELD. CONTRIBUTING FACTOR WAS MY MISPLACED OR INAPPROPRIATE ATTEMPT TO BE 'SMOOTH' IN THE RECOVERY ACTIONS FOR PAX COMFORT RATHER THAN AN ABRUPT MANEUVER TO STOP THE WARNINGS. ALSO; CONTINUOUS AND LOUD GPWS WARNINGS WERE ADDING TO MUCH CONFUSION IN THE COCKPIT. SUPPLEMENTAL INFO FROM ACN 274830: NEGATIVE FACTORS THAT EFFECTED THE SIT WERE THE TSTMS IN THE AREA AND THE RAIN SHOWERS THAT WE WERE FLYING IN AT THE TIME. POSITIVE FACTORS: VERY FAMILIAR WITH DEN SO THAT I HAD THOUGHT ABOUT THE POSSIBILITY OF A WARNING AND THAT WE MIGHT HAVE TO RESPOND TO A WARNING; I BELIEVE LET THE FO DO A BETTER JOB BY NOT BEING TOTALLY SURPRISED WHEN IT DID OCCUR.