On June 21, 1995, at 1745 hours Pacific daylight time, a Cessna 310, N5302A, overran the runway while landing at Las Vegas- Henderson Sky Harbor Airport, Henderson, Nevada. The aircraft was substantially damaged and neither the pilot nor his pilot rated passenger were injured. The aircraft was privately owned and operated, and was on a personal flight when the accident occurred. The flight originated in Henderson at 1715. Visual meteorological conditions prevailed and no flight plan had been filed. According to the pilot, the plane had touched down about 1/3 of the way down runway 36, a 5,000-foot asphalt-surfaced runway. He allowed the aircraft to roll about 2/3 of the way down the runway and then began to apply the brakes. He applied full brake pressure and pumped the brakes, but did not achieve any braking action. He asked his pilot-rated passenger to apply the brakes on his side, but that too was ineffective. When it became apparent that the aircraft was about to overrun the departure end of the runway, the passenger pulled the mixtures to the idle cutoff position. The aircraft continued straight ahead until striking a dirt embankment. The pilot then turned off the magnetos and master switches. The passenger stated that the aircraft touched down at a point about 1/3 down the runway and at a speed he described as "a little bit fast." The passenger then suggested a full stop, to which the pilot agreed. Somewhere beyond the midfield point the pilot asked "could you help me out here?" The passenger asked if he had any brakes and the pilot replied "no." The passenger attempted to apply the brakes from his side and as he did, the aircraft yawed slightly to the left and the left brake responded a little bit. He then pumped the brakes, which he said resulted in even less braking action on the left and still nothing on the right. He asked the pilot to pump the brakes on his side. The pilot replied "I'm trying." When it became apparent that the aircraft was about to overrun, he pulled the mixture controls to the idle cutoff position. As the aircraft approached the departure threshold, he tried for the last time to apply the brakes, but again without effect. A postaccident inspection of the aircraft revealed the nose gear had collapsed and that there was also damage to the left main gear. There were no flat spots found on either of the main tires, nor visible skid marks on the runway. The runway was reported as dry and free of foreign material that might adversely effect braking action. Winds were generally from the northeast with a velocity of less than 5 knots. The pilot claimed brake failure during the landing roll caused the aircraft to run off the departure end of the runway. An inspection of the brake system by Federal Aviation Administration inspectors failed to identify any discrepancies. The manufacturer reported that there are no service difficulty reports on the Cessna 310 braking system. The FAA Information Management System also reported that there are service difficulty reports on the braking system.