An analysis is carried out in order to examine the effects of non-uniform heat source and thermal radiation on the transient free convective MHD flow past a vertical plate. In this model, an inclined magnetic field with periodic heat flux along the wall is included. The governing equations (in non-dimensional shape) are solved numerically by a fully implicit finite difference scheme. A parametric study is performed in order to illustrate the influences of the model dimensionless parameters, namely, the magnetic parameter, the heat source term, the Grashof number, the Prandtl number, and the radiation parameter. The velocity field and the temperature field are evaluated for several amounts of these parameters. The obtained numerical results are compared with the analytical solution in case of constant heat flux with no heat source, and a full agreement was found.