An irreversible cycle model is developed for predicting the performance of a Stirling refrigerator using an ideal or Van der Waals gas as the working substance. The basic irreversibilities included in the cycle model result from the finite rate heat transfer in two isothermal processes, regenerative losses in two constant volume processes and heat leak losses from the heat sink to the cooled space. Two different regenerative forms are discussed, where one is that the time of the regenerative processes is directly proportional to the temperature difference of the working substance in two isothermal processes, and the other is that it is directly proportional to the. time of two isothermal processes. The power input of the Stirling refrigerator is optimized under a given cooling rate. The power input versus cooling rate curves and the coefficient of performance versus cooling rate curves are presented. The maximum cooling rate and coefficient of performance are calculated. Of her optimum performances are also discussed.