In the present study, we analyze the effects of partial slip on steady boundary layer stagnation-point flow of an incompressible fluid and heat transfer towards a shrinking sheet. Similarity transformation technique is adopted to obtain the self-similar ordinary differential equations and then the self-similar equations are solved numerically using shooting method. This investigation explores the conditions of the non-existence, existence, uniqueness and duality of the solutions of self-similar equations numerically. Due to the increase of slip parameter (delta), the range of velocity ratio parameter (c/a) where the similarity solution exists, increases. (C) 2010 Elsevier Ltd. All rights reserved.