MD88 ACFT LNDG ON WET RWY AND USING MEDIUM AUTOBRAKES; RPTR CAPT PERCEIVED THAT ACFT WASN'T DECELERATING QUICKLY ENOUGH AND APPLIED HEAVIER BRAKING MANUALLY. WHEN STARTING TO EXIT THE RWY THE FLC FELT VIBRATION; MORE THRUST REQUIRED AND ACFT LISTING TO THE R. TWR WAS NOTIFIED WHO CLOSED THE RWY AND SENT OUT THE EMER EQUIP. BOTH R MAIN TIRES HAD BLOWN. PAX AND BAGGAGE WERE OFF LOADED PRIOR TO TOWING THE ACFT.

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FLT FROM ATL TO DCA ON MAR/XX/98. I SERVED AS CAPT/PIC OF THAT FLT AND ALSO PF. DCA WX WAS RPTED VIA ATIS AS 900 FT OVCST; VISIBILITY 5 MI; LIGHT RAIN; WINDS 080 DEGS 13 KTS. WE BRIEFED FOR AND RECEIVED VECTORS FOR THE ILS (RWY 36) APCH. THE BRIEFING INCLUDED THE USE OF MEDIUM AUTOBRAKES. WE INTERCEPTED THE LOC AND DCA TWR ADVISED THAT THE RWY WAS WET. BUG SPD FOR THE 40 DEG FLAP LNDG WAS 134 KTS. WE INTERCEPTED AND FLEW THE GS; BREAKING OUT AT APPROX 800 FT MSL. TOUCHDOWN OCCURRED ON SPD AND IN THE TOUCHDOWN ZONE APPROX 1000 FT DOWN THE RWY. I WAS NOT SATISFIED WITH THE ACFT'S RATE OF DECELERATION AND I APPLIED MANUAL BRAKING WELL BEFORE THE 3000 FT REMAINING POINT. NOTING FAIR TO POOR BRAKING ACTION; I APPLIED STEADILY INCREASING BRAKE PRESSURE. THE ANTI-SKID SYS DID NOT SEEM TO BE CYCLING; BUT THE ACFT DID CONTINUE TO SLOW. I NOTICED SOME MILD VIBRATION WHICH SEEMED APPROPRIATE TO THE AMOUNT OF BRAKE APPLICATION. I SLOWED TO NORMAL TAXI SPD FOR A 90 DEG L TURN TO TXWY J AT THE END OF RWY 36. I INSTRUCTED THE FO TO RPT FAIR BRAKING ACTION TO THE TWR. WHILE EXITING THE RWY; I NOTED MODERATE VIBRATION; HIGHER THAN NORMAL THRUST REQUIREMENT TO TAXI; AND A SLIGHT LISTING OF THE ACFT TO THE R. MY INITIAL ASSESSMENT WAS THAT WE MAY HAVE BLOWN ONE OR MORE TIRES. DUE TO THE UNCERTAIN CONDITION OF THE LNDG GEAR; I ELECTED TO STOP THE ACFT PRIOR TO COMPLETELY CLRING THE RWY. WE NOTIFIED TWR OF OUR SIT; THEY CLOSED THE RWY AND THE EMER EQUIP RESPONDED. WE INFORMED THE PAX AND RAMP PERSONNEL OF OUR STATUS. MAINT ADVISED US THAT BOTH R MAIN LNDG GEAR TIRES HAD BLOWN. WE STARTED THE APU AND SHUT DOWN THE ENGS. THE PAX AND BAGGAGE WERE OFF LOADED AT THAT POINT. MAINT PERSONNEL XFERRED FUEL FROM THE R MAIN FUEL TANK TO REDUCE WT ON THE R MAIN LNDG GEAR; AND THE ACFT WAS TOWED CLR OF THE RWY TO A NEARBY PAD. THE ACFT WAS RELEASED TO MAINT. THE FO AND I DEBRIEFED WITH THE DCA STATION MGR; AND I CONTACTED THE APPROPRIATE FLT OPS MGMNT PERSONNEL.