A performance analysis based on the maximum power density criterion has been carried out for an irreversible regenerative reheating Joule-Brayton engine. The obtained results were compared with those obtained using the maximum power performance criterion. The design parameters under the optimal conditions have been derived analytically and their effects on the engine's performance have been discussed. The overall effects of reheating, regeneration and internal irreversibilities are investigated. The obtained results may provide a general theoretical tool for the optimal design and operation of real non-regenerative and regenerative reheating gas turbines.