On April 5, 2001, about 1300 eastern daylight time, a Stinson 108-3, N980C, was substantially damaged while landing at Falmouth Airpark (5B6), Falmouth, Massachusetts. The certificated commercial pilot was not injured. Visual meteorological conditions prevailed and no flight plan was filed for the flight that originated from Katama Airpark (1B2), Edgartown, Massachusetts. The personal flight was conducted under 14 CFR Part 91. The pilot stated that earlier in the day, he departed 5B6 and flew to 1B2. During the initial departure from 5B6, the wind favored runway 25, which was 2,300 feet long and 40 feet wide. The pilot further stated that there were two windsocks at 5B6; one on a hangar, and one surrounded by trees at the approach end to runway 25. The pilot stayed at 1B2 for approximately 90 minutes, and returned to 5B6. During the return flight, the pilot monitored the Martha's Vineyard Airport (MVY), Vineyard Haven, Massachusetts, automated terminal information service (ATIS), and the reported wind was from 340 degrees. During his first attempt to land on runway 25, the pilot felt that he was "too fast, like he had a tailwind." He performed a go-around, and observed that the windsock near the trees was "limp." He did not recall observing the second windsock located on top of a hangar. During the second attempt, the pilot landed on landed on runway 25. However, the wind pushed the empennage to the left, and the airplane departed the right side of the runway. The right wing struck a tree, and the airplane came to rest. After the accident, the pilot observed that the windsock on the hangar was favoring runway 07, at 5-7 knots. The pilot added that in retrospect, he should have landed on runway 07. The reported wind at an airport about 13 miles to the east of 5B6, at 1256, was from 030 degrees at 13 knots, gusting to 19 knots. MVY was located on an island, about 13 miles south of 5B6. The reported wind at MVY at 1235, was from 360 degrees at 12 knots, gusting to 18 knots.