A B737 ENCOUNTERED SEVERE TURB ON APCH WITH A STALL WARNING. DURING THE GAR THE ASSIGNED ALT WAS EXCEEDED BY ABOUT 800' DURING A 6;000 FPM CLB.

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I WAS THE PF. WE WERE BEING VECTORED FOR AN ILS TO RWY 12R. ON DOWNWIND AND BASE TO FINAL; WE WERE EXPERIENCING CONTINUOUS MODERATE TURB. AT APPROX 4 MI ON FINAL (LOC CAPTURE) SEVERE TURB WAS ENCOUNTERED. I GOT THE STICK SHAKER FOR APPROX 1-2 SECONDS AND A GAR WAS INITIATED. DURING THE GAR (APPROX 4200-4500 FT MSL) WE WERE GIVEN A 050 DEG HDG AND CLB TO 5000 FT. THE VVI WAS PEGGED AT 6000 FPM CLB. I RECOVERED THE ACFT AT APPROX 5700-5800 FT AND INITIATED A CORRECTION BACK TO 5000 FT MSL. NO KNOWN ATC ISSUES ON THE GAR AND THEY WERE INFORMED OF OUR DEV. RECOVERED UNEVENTFULLY TO OUR DEST. SUPPLEMENTAL INFO FROM ACN 774337: ON ARR; FRONT WAS APCHING ARPT BUT RADAR INDICATED STRONG CELLS STILL NW ON THE ILS TO RWY 12R. WE ARRIVED FROM S DUE TO ATC ROUTING TFC AWAY FROM STORMS. ON DOWNWIND; NO SIGNIFICANT WX WAS SEEN BUT AS WE WERE NEAR A POS TO TURN BASE; ATC TURNED US 20 DEGS L WHICH TOOK US TOWARD A CELL. WE WERE ON A R DOWNWIND CLOSE TO ARPT AND CTLR MIGHT HAVE TAKEN US WIDER TO MAKE TURN TO FINAL. RIDE DETERIORATED TO CONSTANT MODERATE TURB AS WE CONFIGURED FOR LNDG AND TURNED BASE. WE WERE THEN GIVEN AN INTERCEPT HDG AND INTERCEPTED FINAL. WE THEN ENCOUNTERED SEVERE TURB. INSTS WERE DIFFICULT TO READ AND DIFFICULT TO CHANGE RADIO FREQ TO TWR. FO WAS FLYING AND WAS WORKING THRUST LEVERS TO MAINTAIN AIRSPD BUT WE EVENTUALLY GOT THE STICK SHAKER UPON WHICH I ORDERED A GAR. AS WE INITIATED MISS APCH; TOLD TWR WE WERE IN SEVERE TURB AND THEY HANDED US OFF TO DEP. I TOLD THEM WE NEEDED TO GO L AND NEEDED AN ALT ASSIGNMENT. THEY GAVE US A 050 DEG HDG AND 5000 FT. WE CONTINUED TO STRUGGLE WITH THE AIRPLANE GETTING IT CLEANED UP AND TURNED. WE WERE STILL IN SEVERE TURB (THIS WOULD BE 60-90 SECONDS AFTER GAR). MY ATTN WAS ON RADAR TO GET A CLR AREA AND WHEN I CHKED ALTIMETER WE WERE AT 5900 FT AND I INSTRUCTED FO TO RETURN TO 5000 FT AND ADVISED ATC WE WERE RETURNING TO 5000 FT. THEY ACKNOWLEDGED AND CONTINUED VECTORING US AWAY FROM WX. THIS EPISODE LASTED APPROX 2 MINS AS DID THE SEVERE TURB. NO TFC AROUND US TO CONFLICT WITH. MY FIRST CONCERN WAS TO KEEP CTL OF ACFT; THEN FLY HDGS AND ALT.