The effect of wave motion on the performance of the falling film absorbers was analytically investigated by solving the combined energy and diffusion equations at a low Reynold’s number (Re = 100) using an Alternating Direction Implicit (ADI) finite difference method. By comparing the results of smooth flow and wavy how it was found that wave motion improved the heat and mass transfer rates despite using a film velocity profile that did not permit mixing. The results supported the findings of other researchers who explained the enhancement of mass transfer at low Re by the convection associated with the vertical component of the velocity. The effects of heat pf absorption (Ha) and Lewis number (Le) on heat and mass transfer were also studied and it was found that a low value of Ha together with a high Le would result in a better concentration variation.