HAWKER 800 FLT CREW EXPERIENCES TWO LEFT MAIN TIRE FAILURES AND A SUBSEQUENT RWY EXCURSION; DAMAGING THE LEFT FLAP ON A TAXIWAY LIGHT.

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THE FLT APPEARED NORMAL UNTIL LNDG AT ZZZ; WHEN BOTH L MAIN TIRES BLEW. FOLLOWING IS A SYNOPSIS OF WHAT HAPPENED. AS WE DEPARTED FROM ZZZ1; AND PUT ON THE MAIN AIR VALVES; WE NOTICED WE SMELLED SOMETHING LIKE ASPHALT. THERE IS CURRENT CONSTRUCTION ON A NEW TXWY AT ZZZ1; SO WE THOUGHT THE SMELL WAS ATTRIBUTED TO THAT. THE FLT OVER TO ZZZ WAS UNEVENTFUL UNTIL TOUCHDOWN. WE MADE A NORMAL APCH; EXCEPT WE CARRIED AN EXTRA 10 KTS BECAUSE OF A GUST FACTOR. AS SOON AS WE TOUCHED DOWN; THE PLANE SHUDDERED BADLY AND BEGAN PULLING OFF TO THE L OF THE RWY. WE DEPLOYED LIFT DUMP AND REVERSE THRUST. I USED THE TILLER TO BRING IT BACK TO THE CTRLINE. WE MANAGED TO BRING THE PLANE TO A STOP; A TXWY OFF FROM RWY XX. I SHUT THE L ENG DOWN. CAPT GOT OUT TO INSPECT WHAT WAS WRONG AND CONFIRMED THAT BOTH L MAIN TIRES HAD BLOWN. CAPT ASKED TO GET IN THE L SEAT; STARTED UP THE L ENG AND TAXIED THE REMAINING 30 FT TO CLR THE RWY; THEN SHUT DOWN BOTH ENGS. THE ARPT OPS MGR DROVE DOWN THE RWY AND BROUGHT US 2 PIECES OF TIRE; AND SAID WE HAD RUN APPROX 1 FT OFF THE RWY; THEN BACK ONTO THE RWY; BUT MEANWHILE HAD KNOCKED DOWN A TAXI LIGHT. WE CONFIRMED THAT THE LIGHT HAD HIT THE L FLAP; MADE A DENT AND A HOLE IN THE FLAP. ALTHOUGH I FEEL WE HANDLED THIS EMER VERY WELL AS A TEAM; IF I HAD IT TO DO OVER AGAIN; I WOULD DISPATCH THE FIRE TRUCKS AND DO AN EMER EVAC. FORTUNATELY; WE DIDN'T NEED THE TRUCKS.