The Generator-Absorber Heat Exchanger (GAX) cycle is a general cycle that can use ammonia-water as a absorption fluid. This cycle has been worked on for many years. In this paper, a modeling method is proposed to analyze the heat and mass transfer characteristics of the GAX absorber. Ammonia-water is used as the solution pair. The thermal properties of the solution pair are calculated by computer programs developed by Klein's group. The ammonia vapor and the solution liquid are in counter-current flow in the absorber, and the coolant flows counter to the solution liquid. In this model, a design method for the GAX absorber is proposed for counter-current flow. Seven fluted tubes were installed vertically within a can in the absorber. The GAX absorber has two different heat transfer modes. One is thin liquid film heat transfer on the wall, and the other is absorption at the interface between the vapor and liquid. The absorber also has mass transfer from the bulk vapor region to the interface. This paper proposes that the heat transfer resistance on the liquid film is very small compared with the coolant side, and the mass transfer in the vapor region has a considerable effect on the absorber size.