In this present work the free convection flow and mass transfer over a vertical plate in with radiation and uniform transpiration, the surface of which is exposed to a constant wall temperature. The semi-similar solution of the Navier-Stokes equations, energy and concentration equations has been obtained numerically using by the implicit finite difference scheme of Crank– Nicolson’ s type. Numerical results are presented by velocity, temperature and concentration distributions of the fluid for a wide range of radiation parameter, thermal Grashof number, mass Grashof number, Prandtl number and Schmidt number. The local skin friction, Nusselt number and Sherwood number are also presented graphically. It is observed that, when Prandtl number increases the velocity and temperature decrease in the boundary layer. Also, it is found that as increase in the radiation parameter leads to increase in the velocity field and rise in the thermal boundary thickness.