An investigation is made for analyzing the behavior of MHD flow phenomena of a non-Newtonian fluid over a non-linear radially stretching sheet by using numerical technique. Magnetic field is considered in normal direction to the stretching sheet. With use of similarity transformations, the pdes are transformed into odes. The solution of theses odes are performed by using fourth order Runge - Kutta method along with shooting technique. The significance of different physical parameters characterizes the flow phenomena are analyzed with the use of graphs. The Jeffrey parameter and magnetic parameter has significant effect on velocity and temperature distribution over a non-linear stretching sheet. It is noticed that, the higher magnetic parameter results the increase in entropy generation number where the opposite nature is noticed in the case of Bejan number.