The pilot reported that when the airplane touched down on the runway he felt a vibration followed by the airplane pulling to the left. The pilot added right brake in attempt to realign the airplane; however, it continued to the left and exited the left side of the runway. The airplane traversed over the gravel adjacent to the runway and into brush, where it came to rest. Post accident examination of the airplane by a Federal Aviation Administration inspector revealed that the airplane’s left main landing gear tire was flat. No other anomalies were noted that would have precluded normal flight.