The ideal three-heat-reservoir cycle with constant internal irreversibilities and external heat transfer irreversibilities is used to model the absorption refrigeration machine of a solar operated absorption cooling system. Analytical expressions are obtained for the variation of the entropy transfer with storage tank temperature and the variation of the coefficient of performance (COP) with the cooling capacity of the plant. These expressions give the operating points for the maximum cooling capacity and the maximum COP. The results for ideal irreversible cycles are compared with those obtained by detailed simulation of the absorption cooling system. The effect of internal and external irreversibilities on the second-law efficiency of the plant is examined. The ideal cycles that include internal and external irreversibilities are found to give realistic limits and trends for the cooling capacity and the COP of solar powered absorption cooling systems.