The flow and heat transfer of a non- Newtonian power-law fluid over a non-linearly stretching surface has been studied numerically under conditions of constant heat flux and thermal radiation and evaluated for the effect of wall slip. The governing partial differential equations are transformed into a set of coupled non-linear ordinary differential equations which are using appropriate boundary conditions for various physical parameters. The remaining set of ordinary differential equations is solved numerically by fourth-order Runge–Kutta method using the shooting technique. The effects of the viscosity, the slip velocity, the radiation parameter, power-law index, and the Prandtl number on the flow and temperature profiles are presented. Moreover, the local skin friction and Nusselt numbers are presented. Comparison of numerical results is made with the earlier published results under limiting cases.