Steady-state conjugate natural convection in a square cavity filled with a porous medium is studied numerically in this paper. The enclosure consists of two horizontal conductive walls of finite thickness and two vertical walls at different uniform temperatures. The focus is on the role of solid-fluid conductivity ratio, k, on the flow and heat transfer characteristics and the average Nusselt number, \(\), over the vertical hot and cold walls of the cavity for a limited set of particular parameters. It was shown that the interface temperature, θw, along the top of the solid wall decreases with the increase in the wall conductivity k. Also, the values of \(\) decreases with the increase of the values of the parameter k. Comparison with known results from the open literature when the wall thickness of the horizontal solid walls is neglected (non-conjugate problem) is excellent.