The endoreversible cycle model of refrigerators is extended to an irreversible cycle model which includes the irreversibility of finite-rate heat transfer and the internal irreversibility of the working fluid. The cycle model is then used to analyze the optimal performance of refrigerators. For a specified cooling rate and a given overall heat transfer area of the two heat exchangers, minimizing the coefficient of performance of refrigerators leads to an optimal ratio of the two heat exchanger areas.