A mathematical model based on the lubrication approximation which defines absorptive property of a substrate using a Darcy's model is presented. This numerical model is verified with the help of comparison between the analytical and numerical solutions for the absorption of thin film on horizontal porous substrates. Results show that physical properties of the substrates, i.e., permeability, porosity, capillary pressure and equilibrium contact angle, affect the rate of absorption of the fluid. Adding inclination to the problem introduces the gravitational pull in the absorption dynamics. This directly shows its effects on the footprints formed inside the porous substrates.