On October 7, 2004, at approximately 1335 mountain daylight time, a Cessna 172N, N73764, piloted by a solo student pilot, was substantially damaged when it made a hard landing at the Natrona County International Airport (CPR), Casper, Wyoming. Visual meteorological condition prevailed at the time of the accident. The personal flight was being conducted under the provisions of Title 14 CFR Part 91 without a flight plan. The pilot reported no injuries. The flight originated at CPR at 1300. The student pilot was performing her fourth touch-and-go landing on runway 21 (10,600 feet by 150 feet, dry asphalt), when she allowed the airplane to touch down hard on the runway. The pilot said everything was fine until she got into the flare. She said that she felt she was going to float so she "put in some power." She said she felt she had things under control, so she reduced the throttle to idle. When the airplane touched down, it bounced. The pilot said she released a little back pressure. "The second time it [the airplane] came back to the ground, it bounced hard, and this time I think the propeller hit. It bounced hard 3 or 4 times after that. Back and forth." The pilot said she finally got the airplane stopped. She contacted the tower and received permission to taxi back to the ramp. An inspection of the airplane revealed that the airplane's nose gear was bent aft and the firewall was buckled in several places. One propeller blade was bent aft at the tip. The student pilot's instructor reported the pilot was an average to medium skilled student. The student pilot had soloed two times previously.