On May 8, 1995, about 1342 Alaska daylight time, a wheel equipped Piper PA-31-350 airplane, N3588Z, lost a portion of the right main landing gear leg when it struck a snow berm during takeoff from a gravel airstrip at Toksook, Alaska. The airplane sustained substantial damage during the subsequent intentional gear-up landing at the Dillingham Airport, Dillingham, Alaska. The airline transport certificated pilot and five passengers aboard were not injured in the mishap. The 14 CFR Part 135 on-demand air taxi flight operated in visual meteorological conditions. A company VFR flight plan was filed. The pilot reported he was dispatched to Toksook to pickup an unknown number of passengers. He loaded five passengers and luggage, and estimated the gross weight of the airplane prior to takeoff to be 6200 pounds. He elected to take off to the north to avoid a reported soft spot at the south end of the runway. Runway 15-33 is 1,800 long, and slopes uphill to the north with a gradient of approximately 2%. During the takeoff roll, the pilot said the airplane encountered a soft spot in the runway which caused the airplane to decelerate. He continued the takeoff, but the right main landing gear tire struck a snow berm shortly after liftoff. The pilot said he continued to Dillingham, and noted that the green, right main landing gear "down" light failed to illuminate when the gear handle was selected to the down position. After conferring with the company's Director of Maintenance, it was decided to perform a gear up landing. The pilot reported he feathered both engines prior to landing, and a smooth, uneventful landing ensued. Examination of the fuselage disclosed that several of the belly bulkheads were damaged, as well the majority of the belly skin. A review of the performance data contained in the Pilot Operating Handbook (POH) for the Piper PA-31-350, disclosed no formula for computing takeoff distance from other than hard surfaced runways, nor was any data available for takeoff with an upslope gradient. Computations provided by the FAA Principal Operations Inspector assigned to the company, indicated that the accident airplane weighed an estimated 6,576 pounds at takeoff. The inspector wrote in his report to the NTSB, that at a weight of 6,576 pounds, the accident airplane would have required a minimum,level, hard surfaced runway length of 2,200' to takeoff.