The three dimensional flow and heat transfer of a non-Newtonian incompressible viscoelastic electrically conducting fluid past a porous stretching/shrinking sheet is investigated in the current paper. The essential target, unlike the numerical works in the literature, is to search for the occurrence of exact solutions. Unique solutions determined under the assumptions of usual boundary layer theory are given for a particular case, akin to the axisymmetric flow in the absence of wall suction or injection. The analysis of heat transfer is also performed. The exact form of velocity/temperature profiles and the coefficients of skin friction/heat transfer enables one to easily seize the physical processes occurring in the presented model with several effects taken into account. The provided formulas will be beneficial to the future research in this arena. (C) 2014 Elsevier Ltd. All rights reserved.