In this paper we investigate the steady, two-dimensional, free convection flow caused by a sinusoidally heated and cooled infinite vertical surface that delimits a semi-infinite porous media. An analytical solution which is valid for small values of the Rayleigh number, Ra, is obtained using a regular perturbation method. A finite-difference technique is used to numerically solve the problem for 0 less than or equal to Ra less than or equal to 150 and for small Values of Ra, the results are in very good agreement with the analytical solutions and the streamlines are in the form of a row of counter rotating cells which are situated close to the vertical surface. As the Rayleigh number increases, above a value of about 40, then the cellular Row separates from the plate. At very large values of Ra, a scaling analysis has been performed and the results suggest that the vertical velocity and the local Nusselt number on the plate support better the boundary-layer scalings, than does the mean vertical velocity and the mean Nusselt number along the plate. In the situation in which the flow separates, i.e. for Ra greater than or similar to 40, the smallest possible solution domain must be chosen, by using the symmetry of the problem, otherwise it has not been possible to obtain a convergent numerical solution.