In order to clarify the behavior of falling films in the absorber of absorption chillers, numerical analysis of the falling films in the transition regions was performed. Since the treatment of the surface becomes difficult in x-y cooridinates, y coordinates are normalized by the film thickness to fix the surface. The fundamental equations are changed into conservative forms by the method of Shyy et al. before discretization. The critical wavelengths for an aqueous solution of lithium bromide and water were determined by the proposed method. The film Reynolds numbers were varied in the range of 10-200. For a few cases in the unstable region, the waveforms are calculated for the initial disturbance of 10% of average film thickness. As they grow, slopes of waves become steeper at the front, and for Ref =100, film is divided into a thin base film of uniform thickness and a liquid mass sliding on it.