An irreversible simplified model for a Stirling cryocooler is presented in this paper. This model takes into account the finite-rate heat transfer, finite-time evolution of the cycle's regenerative processes and the friction irreversibility. The maximum cooling load and the corresponding coefficient of performance (COP) at the maximum cooling load are derived. The effects of the regenerative time, finite-rate heat transfer and friction on the optimal COP at the maximum cooling load are found. A numerical example demonstrates the relation between the cooling load and the COP.