A quadratically stretching/shrinking surface of two dimensional magnetohydrodynamics stagnation point flow is investigated numerically. The velocity of the surface is assumed in quadratic form and subject to a linear mass flux. The influences of the governing parameters namely stretching/shrinking parameter , suction/injection parameter S, fluid temperature index m, and magnetic parameter M on the flow and thermal fields are studied. The model of nonlinear ordinary differential equations is obtained by reducing the partial differential equations of the boundary layer using an suitable similarity transformation. The equations are then solved numerically by boundary value problem solver, bvp4c built in MATLAB software. The numerical results are verified by comparing them with previously reported results. The characteristics of the flow and heat transfer characteristics are shown graphically and analyzed for distinct values of the governing parameters. It is found that both magnetic and temperature index parameters reduce the velocity flow while the magnetic parameter enhances the heat transfer rate. There exist dual solutions for certain range of. A stability analysis is performed to determine which of these solutions are stable and which are not. © Published under licence by IOP Publishing Ltd.