On July 5, 2010, at 1400 mountain daylight time, N71784, a Cessna 182, landed hard and bounced while landing at Alamogordo-White Sands Regional Airport (KALM), New Mexico. The airplane was registered to and operated by White Sands Soaring Association, Alamogordo, New Mexico. The commercial pilot was not injured. Visual meteorological conditions prevailed and no flight plan was filed for the glider towing flight conducted under 14 Code of Federal Regulations Part 91. The pilot reported that he was returning to land after towing a glider to altitude. He said the wind was gusting to 19 knots between 290 and 010 degrees. The pilot made two attempts to land on Runway 03 but elected to go-around each time due to a shimmy in the main landing gear. On the third attempt to land, he switched to Runway 34 (a dirt runway). During the landing he bounced and elected to go around. The pilot was convinced there was something wrong with the landing gear so he did a low approach over Runway 21 and asked for ground personnel to visually check the gear. Ground personnel said the gear looked fine. The pilot made another attempt to land on Runway 34 and "bounced really hard 2-3 times." Again, the pilot elected to go-around and decided to try another landing on Runway 03. After landing, the pilot reported that there was still a shimmy and the airplane veered toward the right side of the runway. As the plane slowed down, the pilot was able to taxi the airplane safely back to the ramp. A Federal Aviation Administration (FAA) inspector performed an examination of the airplane. He reported that the firewall was wrinkled, the engine mounts were deformed, the fuselage was damaged at the waterline, the propeller was damaged, and the nose gear mount bracket was pushed up into the fuselage. Flight control continuity was confirmed. No anomalies were found with the engine or other airplane systems.