The effect of radiation and variable viscosity on a MHD free convection flow past a semi-infinite flat plate with an aligned magnetic field has been studied in the case of unsteady flow. The plate is moved with a constant velocity, which is in the same or opposite direction to the free stream velocity. The fluid viscosity is assumed to vary as an inverse linear function of temperature. The effect of the induced magnetic field has been included in the analysis. The governing partial differential equations have been solved numerically using the finite difference method. The velocity, the x-component of the induced magnetic field and heat transfer characteristics of the flow are determined