Air dehumidification by a liquid desiccant falling on rectangular finned-tubes arrangements was numerically studied for different air flow arrangements: parallel, counter and cross flow with respect to the desiccant liquid film. Heat and vapor transfer between desiccant film, air and the finned-tube arrangements were investigated. Governing equations which relate air temperature, air humidity, liquid desiccant temperature, liquid desiccant concentration and finned-tubes surface temperature were derived and solved using finite difference technique. The effects of air/desiccant inlet conditions and the temperature of the fin-tube arrangement on air dehumidification, heat and vapor transfer were predicted for the different flow arrangements. The results show that (i) the parallel flow arrangement gives more cooling and dehumidification rates, (ii) for all flow arrangements, the outlet air temperature and air humidity, increases/decreases with increasing mass flow rate of air and liquid desiccant in cooling-dehumidification/desiccant regeneration processes. Correlations for heat and vapor transfer in air cooling-dehumidification and desiccant regeneration processes were predicted for the different flow arrangements.