ON LNDG; A CE550 BLEW BOTH MAIN TIRES WHICH WAS CAUSED BY A PARTIALLY ENGAGED PARKING BRAKE. THE REPORTER SUSPECTS THAT THE PARKING BRAKE CABLE WAS BINDING AND NOT COMPLETELY RELEASED. THERE IS NO WARNING SYSTEM OR LIGHT THAT INDICATES THE PARKING BRAKE IS STILL ENGAGED.

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UPON TOUCHDOWN IT WAS EVIDENT THAT THE MAIN LNDG GEAR WAS SKIDDING. WE MADE A NORMAL VISUAL APCH TO A NORMAL LNDG ON THE BLOCKS. ALL CHKLISTS WERE COMPLETED INCLUDING ENSURING THE PARKING BRAKE WAS OFF. (ACFT SEEMED NOT TO ACCELERATE NORMALLY ABOVE 80 KTS ON OUR TKOF SO WE BRIEFED ABOUT LNDG WITHOUT THE ANTISKID BUT HAD NO FAILURE LIGHT FOR ANY SYSTEMS.) AFTER LNDG; TWR CALLED STATING MUCH SMOKE AND DEBRIS WAS COMING FROM REAR OF THE ACFT AND ASKED IF WE NEEDED ASSISTANCE THEN SAID THEY WERE ROLLING THE FIRE TRUCKS. I STATED WE MUST HAVE BLOWN A TIRE. UPON EXITING ACFT AFTER SKIDDING TO A STOP; WE FOUND BOTH MAIN TIRES BLOWN. THE EVENT CLOSED THE RWY FOR APPROX 2 HOURS WHILE MAINT REPLACED THE WHEELS/TIRES AND TUGGED ACFT OFF RWY. NO ONE WAS INJURED. IT WAS LATER DETERMINED THAT THE PARKING BRAKE CABLE COULD BIND AND REMAIN PARTIALLY ENGAGED AND THAT IS ASSUMED TO HAVE HAPPENED. UPON SUBSEQUENT FLTS; WE REMAINED VIGILANT TO ENSURE KNOB IS TOTALLY IN BEFORE TAXI/TKOF. THE NEXT DAY AFTER REPLACING WHEELS AND TIRES THE ACFT OPERATED NORMALLY BUT THE PARKING BRAKE CABLE DOES BIND OCCASIONALLY. I ALSO FLY LEAR 35'S AND THEY HAVE A BRAKE ENGAGED LIGHT THAT WOULD BE HELPFUL ON THE CITATION.CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: THE RPTR STATED THAT THE PARKING BRAKE IS LOCATED BEHIND THE CAPT'S YOKE JUST UNDER THE LOWER EDGE OF THE INSTRUMENT PANEL AND HAS A KNOB ON THE CABLE ABOUT THE SIZE OF A HALF DOLLAR COIN. IT HAS NO WARNING LIGHT WHEN THE BRAKE IS APPLIED FULLY OR PARTIALLY. THE FO IS UNABLE TO SEE THE POSITION OF THE CABLE. BOTH MAIN TIRES WERE BLOWN AND WERE REPLACED. THIS IS THE FIRST PARKING BRAKE INCIDENT THE RPTR HAS EXPERIENCED BUT IS AWARE OF ANOTHER INCIDENT ON ANOTHER CE550 WITH A PARTIALLY APPLIED PARKING BRAKE.