This paper is devoted to introduce a numerical simulation using finite difference method with the theoretical study for the problem of the flow and heat transfer over an unsteady stretching sheet embedded in a porous medium in the presence of a thermal radiation. The continuity, momentum and energy equations, which are coupled nonlinear partial differential equations are reduced to a set of two nonlinear ordinary differential equations, before being solved numerically using an implicit, iterative finite difference method (FDM). The accuracy of the proposed method is tested by performing various comparisons with previously published work and the results are found to be in an excellent agreement. The effects of various parameters like the Darcy parameter, the radiation parameter and the Prandtl number on the flow and temperature profiles as well as on the local skin-friction coefficient and the local Nusselt number are presented and discussed