A BE-58 suffered a flat right main gear tire failure at or prior to landing. The aircraft was stopped on the runway and towed for repair/replacement.

Narrative

A flat tire was experienced upon landing. Upon rotation at the departure airport a vibration was felt that caused suspicion of the aircraft's tire conditions. The Tower was notified of the pilot's suspicion. And an airport vehicle made two sweeps of the runway and found no tire debris. When the aircraft left the ramp the tires were in good condition and correctly inflated. Nothing abnormal was felt during taxi and there were no notable occurrences that would have caused the tire to go flat.Once airborne the aircraft behaved normally. Enroute we discussed procedures to deal with the possible problems. The landing was smooth and for the first seconds after touchdown the tires seemed to be functioning properly. The vibration was then felt again and began to strengthen in intensity. Aggressive control inputs were required to keep the airplane on the runway. We attempted to make a taxiway turnoff with the aircraft's momentum but it was not possible. The aircraft stopped short of the taxiway on the right side of the runway. Upon inspection we discovered the right main tire was flat. The tire could not be changed on the runway and the aircraft was; therefore; towed; off and the tire changed. This did not cause damage to the aircraft.Although an accident was avoided in this case; it was potentially a very dangerous situation in which the pilot had little control. If the tire problem had been diagnosed earlier in the takeoff roll the takeoff could have been aborted. We believe the tire must have been punctured during or shortly before the takeoff roll. More care should be taken to remove objects from airport surfaces that are hazardous to tires.