Absorption cooling cycles have the advantage of being environmental and using solar or waste heat for cooling with very small electric power. This work presents exergy analysis of a double effect parallel flow absorption system. For the exergy analysis a computer program is developed for the thermodynamic properties of lithium bromide-water solutions by the author in FORTRAN codes. The exergy analysis of the cycle has showed that the exergetic coefficient performance (ECOP) is about 0.28 and that means the cycle is an efficient cycle. The exergy destruction of each component of the cycle is calculated. Most of the irreversibilities in the cycle occurred in the evaporator and in the absorber which both is about 74 % of the total irreversibility. That means the efficiency of the evaporator and the absorber is crucial for the double effect absorption cycles. To improve the performance and the working conditions of the cycle better design and improving of these two components is essential.