This communication presents a parametric study of irreversible Stirling and Ericsson cryogenic refrigerator cycles including external and internal irreversibilities along with finite heat capacities of external reservoirs. The external irreversibility is due to finite temperature difference between the working fluid and external fluids in the source/sink reservoirs, while the internal irreversibilities are due to regenerative heat loss and other entropy generations in the cycle. The cooling load is maximized for the given power input. The cooling coefficient of performance, the heat transfers to and from the refrigerator and the working fluid temperatures at these conditions have been evaluated. The effect of different parameters (reservoirs fluid temperature, the effectivenesses, heat capacitance rates of the external reservoirs and irreversibility parameter) on the performance of these cycles has been studied. It is found that the effect of the internal irreversibility parameter is more pronounced than that of other parameters.