An analysis is carried out to study the flow, chemical reaction and mass transfer of a steady laminar boundary layer of an electrically conducting and heat generating fluid driven by a continuously moving porous surface embedded in a non-Darcian porous medium in the presence of a transfer magnetic field. The governing partial differential equations are converted into ordinary differential equations by similarity transformation and are solved numerically by using the finite element method. The results obtained are presented graphically for velocity, temperature and concentration profiles, as well as the Sherwood number for various parameters entering into the problem.