Absorption of water vapor into LiBr-$H_2O$ O solution flowing over a finned inclined surface is numerically investigated. The momentum, energy, and diffusion equation are numerically solved using a finite difference method. The four different shapes of the wall surfaces are considered to find the best surface for absorption assuming that the wall temperature and the surface tension are constant. The effects of the fin interval and Reynolds number are investigated. Based on the numerical results, it is known that the parabolic surface shows better absorption performance than the other surfaces, and that water vapor absorption increases gradually with decreasing the fin interval.