A theoretical model was developed to investigate a falling-film absorber on horizontal tubes with an aqueous alkaline nitrate solution as working fluid. The absorbent, composed of an aqueous solution of nitrates (Li, K, Na) in salt mass percentages of 53%, 28%, and 19% respectively, offers favourable thermal stability, corrosiveness, and heat and mass transfer conditions which can be appropriate for absorption cooling cycles driven by high-temperature heat sources. The mathematical model developed characterises the heat and mass transfer processes and the flow regime effect (droplet-formation, droplet-fall, and falling-film) on the falling-film absorber. The results show the importance of the falling-film and droplet-formation flow regimes in the absorption process. The solution temperature and concentration profiles inside the absorber were established together with their values at the exit. The results obtained by the theoretical model were well in agreement with the experimental data obtained by the authors in a previous study. Deviations in predicting the solution and cooling water temperatures at the absorber exit were around 1 °C and for the concentration of the solution leaving the absorber, around 0.49%. The mathematical model also predicts the absorption rate at 4.7 g·m−2·s−1 for the absorber design and operating conditions used in the present work. This value is 22% higher than the experimental value obtained by the authors in their previous experimental work. The deviation is attributed to approximations incorporated into the model, especially as regards surface wettability and calculation of the mass transfer coefficients for each flow regime.