Two-dimensional conjugate free convection due to a vertical plate of finite extent adjacent to a semi-infinite porous medium is investigated numerically using finite-difference techniques. Computed solutions to the governing heat and momentum equations are obtained for a wide range of different values of the non-dimensional parameters that are present in the problem, namely the Rayleigh number, Ra, the thermal conductivity ratio, k, between the plate and the porous medium, and the plate aspect ratio, lambda. The results give good agreement with results obtained by other authors for k, Ra >> 1, and compare very Favourably with an approximate analytical one-dimensional analogue which is developed for Ra >> 1.