The four right main body landing gear tires burst during the takeoff ground roll, and the crew performed a precautionary landing. Pieces of the tires and wheel assemblies penetrated the fuselage structure and the airplane incurred substantial damage. Post accident examination revealed that the valve cores on three of the four inflation valves, including the two aft valves, were not torqued to the manufacturer’s specifications and leaked steadily. Examination of the right aft main body landing gear tires (number 11 and 12) showed that they were operated in an over deflected condition at some point prior to the event, which resulted in internal damage to the tires. The aft tires failed first as a result of the internal damage and initiated the accident sequence. Damage to the forward tires was consistent with the tires bursting due to their impact by debris from the aft tires. Probable Cause: the incorrect installation of the inflation valve cores in the number 11 and number 12 wheel assemblies that allowed the tires to be operated in an over deflected condition that resulted in their failure.