The numerical solutions of the system of non linear partial differential equations, which describe the unsteady flow of MHD non-Newtonian fluid with heat and mass transfer past a porous plate through a non-Darcy porous medium are obtained, taking into account the effects of viscous and ohmic dissipations and the chemical reaction. Finite difference method is used for solving the system of equations. The results of the velocity, temperature, concentration distributions, skin-friction, rate of heat and mass transfer are illustrated graphically for different values of physical parameters. Also, the stability condition is studied.