In this study, a steady stagnation point flow due to a permeable shrinking sheet with the slip effects is investigated. Employing similarity transformations, the governing boundary layer equations are transformed into the nonlinear ordinary differential equations. The transformed equations are figured out numerically using the shooting method. Results show that dual solutions for velocity and temperature distribution exist for a certain range of the shrinking parameter. The results also indicate that the skin friction coefficient and the local Nusselt number increase for the upper branch solution as the suction parameter increases. Meanwhile, for the lower branch solution, the skin friction coefficient decreases and the local Nusselt number increases as the suction parameter increases. It is also found that the velocity slip and suction process delay the boundary layer separation whereas the temperature slip does not affect the boundary layer separation.