This article presents a numerical solution for the flow of a Newtonian fluid over an impermeable stretching sheet with a power law surface velocity, slip velocity and variable thickness. The flow is caused by a nonlinear stretching of a sheet. The governing partial differential equations are transformed into a nonlinear ordinary differential equation which is using appropriate boundary conditions for various physical parameters. The numerical solutions of the resulting nonlinear ODEs are found by using the efficient finite difference method (FDM). The effects of the slip parameter and the wall thickness parameter on the flow profile are presented. Moreover, the local skin friction is presented. Comparison of the obtained numerical results is made with previously published results in some special cases, and excellent agreement is noted. The results attained in this paper confirm the idea that FDM is a powerful mathematical tool and can be applied to a large class of linear and nonlinear problems arising in different fields of science and engineering.