In this article we study the onset of thermal convection in a liquid layer overlying a porous layer in the presence of a free surface. The full non-linear two-dimensional Navier Stokes and the Fourier energy equations are solved for the liquid layer. The Brinkman model, together with the energy equation, describes the porous layer. The partial differential equations are solved numerically using the finite element technique. Two cases are presented: In the first case, the finite rectangular cavity is heated from below. The cavity aspect ratio, defined as the ratio of its width to its thickness, is studied in detail. The results are compared to the earlier results of Desaive et al. (2002) who studied a similar situation for layer of infinite lateral extent.