In this paper we investigate the flow and heat transfer of a Jeffrey fluid near the stagnation point on a stretching/shrinking sheet with a parallel external flow. The main concern is to analytically investigate the structure of the solutions which might be unique or multiple. It is shown that structure of the solutions strongly depends on a parameter measuring the ratio of strength of the external flow to surface stretching/shrinking, we name it as stretching strength parameter. When this parameter is set to zero, the solutions evolve into the multiple/triple solutions already given in Turkyilmazoglu (2011) [1,2]. For other values, closed-form formulae for the boundary layer equations of the flow are presented for the Jeffrey fluid. Heat transfer analysis is also carried out for a boundary heating process taking into consideration both a uniform wall temperature and a linearly increasing wall temperature. The flow field is found to be influenced by the presence of physical parameters, stretching/shrinking strength, Deborah number and suction/injection parameters, whereas the temperature field is additionally affected by Prandtl number. The velocity/temperature profiles and skin friction coefficient/Nusselt number are easy to conceive from the exact formulas presented, which also provide benchmark for testing other numerical schemes. (C) 2012 Elsevier Ltd. All rights reserved.