The effects of non-Darcy and heat source on magneto hydrodynamics (MHD) Rivlin-Ericksen fluid of third-grade flow between two vertical flat plates through in a porous medium has been studied analytically and numerically in this paper. The system of highly non-linear partial differential equations is converted to a system of non-linear but ordinary differential equations via the similarity transformation. After that the governing equations are solved analytically using Multi−step differential transform method (MDTM) and numerically using finite difference method (FDM) and shooting technique using Runge-Kutta fourth order. Present study found that (MDTM), (FDM) and shooting are a powerful approach for answering highly non- linear differential equations such as this problem. The effects of different parameters on velocity and temperature are displayed through graphs and tables. Comparisons between current results and available previous results are listed and displayed in figures and tables. Current results prove that the agreement with previous published results.