A numerical solution is presented for unsteady coupled heat and mass transfer by natural convection from a vertical plate embedded in a uniform porous medium in the presence of thermal radiation and chemical reaction effects. The governing equations for this problem were developed and non-dimensionalized and the resulting equations were then solved numerically by an explicit finite-difference scheme. The Roseland approximation is used to describe the radiative heat flux in the energy equation. The solutions at each time step have been found to reach the steady state solution properly. The numerical results are presented in the graphical form to show the effects of material parameters including the thermal buoyancy, the solutal buoyancy, Reynolds number, the inverse thermal radiation parameter, the permeability parameter, Prandtl number, Schmidt number and the chemical reaction parameter on the skin-friction coefficient, the Nusselt number, the Sherwood number, the velocity profiles, the temperature profiles and the concentration profiles in the boundary layer.