In this paper, the effects of suction/blowing and thermal radiation on steady boundary layer stagnation-point flow and heat transfer over a porous shrinking sheet are investigated. The existence of dual solutions, unique solution and non-existence of solution for self-similar equations of the flow and heat transfer are analyzed numerically. It is noted that the range of velocity ratio parameter where the solution exists increases/decreases with increasing suction/blowing. With increasing suction, temperature at the wall is found to increase (decrease) for the first (second) solution. Due to increasing Prandtl number and thermal radiation parameter the thermal boundary layer thickness becomes thinner. (C) 2010 Elsevier Ltd. All rights reserved.