This paper proposes a model of absorption chillers and heat pumps that reduces the characteristics of these machines into two simple algebraic equations: one for the capacity and one for the COP. These equations, however, still contain the complete thermodynamic information of the systems (in a slightly simplified form), and they can be solved analytically. The results obtained with the model deviate only marginally from exact numerical simulations if the range of operating conditions is not too large. Due to its simplicity, the model is well suited to be incorporated as a very stable and fast absorption machine module in energy system simulation packages. A further major benefit is that it is an appropriate tool for fitting catalog data of commercial equipment so that their operating characteristics become available in the computerized form required for system simulation applications. The model has been successfully applied to catalog data of commercial single-effect lithium bromide/water chillers and water/ammonia heat pumps.Units: SI