The heat and mass transfer for an absorption process taking place on a falling film flow in a porous medium is modeled by the Brinkman-Forchhiemer extended Darcy equation and solved numerically. The solutions show that the transport rates are higher than that of a smooth film absorption process without a porous medium. The mass absorption rate increases with increasing solution Bow rate, conductivity ratio and absorber pressure, and is optimum with porosity of 0.9 and conductivity ratio of 10. The correlations of dimensionless heat and mass transfer coefficients are given. These results will be valuable for the design of an absorption cooling system.