The pilot was on a personal sightseeing flight when she realized she was low on fuel, and immediately diverted to an alternate airport. While enroute to the alternate airport she determined that enough fuel remained by consulting her onboard fuel computer, and elected to continue to her destination. As she approached her destination airport, the airplane's engine began to sputter, followed by a total loss of engine power, and she selected a small private airstrip as a landing site. During the emergency descent she "undershot" the landing area, and flared into the trees near the approach end of the runway. The airplane sustained substantial damage to the wings, fuselage and horizontal stabilizer. The pilot stated that there were no preaccident mechanical anomalies with the airplane that would have precluded normal operation, and noted that the loss of engine power was due to fuel exhaustion.