This paper investigates steady laminar boundary layer flow of power law fluids past a flat surface with suction or injection and magnetic effects. A new nonlinear diffusion model is proposed, which takes the effects of power law viscosity on concentration fields into account by assuming that the concentration field is similar to the velocity, with a modified Fick's law of diffusion for power law fluids. The governing strongly nonlinear partial differential equations are reduced into a set of coupled ordinary differential equations and then solved numerically by the shooting technique coupled with the Runge-Kutta scheme and the Newton's method. The effects of the Hartmann number, the suction or injection parameter, the power law index, the concentration power law index, the concentration radio parameter and the generalized Schmidt number on the velocity and the concentration fields are presented graphically and analyzed in detail. (C) 2015 Elsevier Ltd. All rights reserved.