Abstract. In this study, the numerical investigations of the mixed convection on a stagnation point flow past a stretching vertical surface with Newtonian heating is considered. The non linear partial differential equations that governed the model are transformed by similarity variables before being solved numerically using the Keller-box method. The numerical solutions are obtained for the surface temperature, the heat transfer coefficient, the reduced skin friction coefficient and the reduced Nusselt number as well as the velocity and the temperature profiles. The features of the flow and heat transfer characteristics for pertinent parameters which are Prandtl number, stretching parameter, buoyancy parameter and conjugate parameter are analyzed and discussed.