In this paper, the power density, defined as the ratio of power output to the maximum specific volume in the cycle, is set as the objective for performance analysis of an irreversible, regenerated and closed Brayton cycle coupled to constant-temperature heat reservoirs from the viewpoint of finite time thermodynamics (FTT) or entropy generation minimization (EGM). The analytical formulae about the relations between power density and pressure ratio are derived with the heat resistance losses in the hot- and cold-side heat exchangers and the regenerator, the irreversible compression and expansion losses in the compressor and turbine, and the pressure loss in the pipe. The results obtained are compared with those obtained by using the maximum power criterion. The influences of some design parameters, including the effectiveness of the regenerator, the temperature ratio of heat reservoirs, the effectivenesses of heat exchangers between working fluid and heat reservoirs, the efficiencies of the compressor and the turbine, and the pressure recovery coefficient, on the maximum power density are illustrated by numerical examples, and advantages and disadvantages of maximum power density design are analyzed. When heat transfers between working fluid and heat reservoirs are carried out ideally, the results of this paper coincide with those obtained in recent literature.