Detailed numerical calculations are presented in this paper for the steady-state free convection within an inclined cavity filled with a fluid-saturated porous medium. The inclined walls are maintained at constant but different temperatures, while the horizontal walls are adiabatic. To simplify the effort in matching the grid mesh with the inclined walls of the cavity, the computational domain is mapped onto a rectangular shape cavity using a non-linear axis transformation. The governing equations tin the stream function and temperature formulation) are expressed in the new coordinate system and solved numerically using the ADI (Alternative Direction Implicit) finite-difference method. Flow and heat transfer characteristics (stream lines, isotherms and average Nusselt number) are investigated for a wide range of values of the Rayleigh number, inclined angle and cavity aspect ratio. The present solutions for a vertical cavity are compared with the known results from the open literature. It was found that these results are in very good agreement. We believe that these results serve as a reference against which other solutions for the present problem can be compared in the future.