The effects of diffuser shape and back pressure on the performance of closed cycle disk MHD generators are investigated with two dimensional numerical simulations taken account of boundary layer. The enthalpy extraction ratio decreases and fluctuates periodically with increase in the back pressure. The amplitude of power output fluctuation and the period depend on the volume of the inverse flow region. For the reduced height diffuser, the inverse flow region is supressed and the fluctuation becomes smaller than that for the constant height diffuser. When operated with a back pressure lower than an optimum value the diffuser does not work because of reacceralation in the diffuser. For the higher back pressure on the contrary, the inverse flow region propagetes into the MHD channel, then the enthalpy extraction ratio is reduced and the Mach number at the exit of MHD channel becomes lower than unity. For the optimum back pressure, high enthalpy extraction ratio is achieved and the adiabatic efficiecy at the diffuser exit is decreased by several percent from that evaluated at the MHD channel exit.