This communication presents finite time thermodynamic optimization of irreversible cascaded refrigeration and heat pump cycles having source/sink thermal reservoirs of finite heat capacitance. A general expression for the optimum coefficient of performance of the refrigerator/heat pump is derived at minimum power input and given cooling/heating load conditions, respectively. External irreversibility is due to the finite temperature difference between the system working fluids and thermal reservoirs (heat source/heat sink), while internal irreversibility is due to the non-isentropic expansion and compression within the system, which is represented by an irreversibility parameter indicating the deviation from an endoreversible case. It is found that the effect of the internal irreversibility is more pronounced as compared to the external irreversibility. The effect of various operating parameters on the cooling and heating performance of the cascaded refrigeration and heat pump cycles, respectively, is studied and numerical results are presented in the end.