Abstract The steady-state mathematical modelling of advanced absorption cycles can be time-consuming and error-prone. In this work, a computer tool based on a modular approach and supported by a comprehensive methodology is described. The solver automatically eliminates redundant mass and species balance equations, detects the existence of paired interconnections, and identifies the nature of the missing auxiliary conditions. To illustrate the tool's capabilities, two advanced refrigeration cycles are modelled, double-lift and resorption. For each cycle, two different embodiments are discussed in consideration of the volatility of the absorbent. With reference to cooling applications driven by low temperature heat, the performance of three cycles are compared: NH3-LiNO3 double lift (DL1), NH3-H2O double lift (DL2), NH3-H2O resorption (R2). DL1 and DL2, despite their lower thermal COPc can achieve a maximum value of EER (about 7.7) only slightly lower than that achieved by R2 (about 7.9) with a much lower driving temperature.