The flow and heat transfer problem of a Sisko fluid in an annular pipe is considered. The governing nonlinear equation of an incompressible Sisko fluid is modelled. Both analytical and numerical solutions of the governing nonlinear problem are presented. The analytical solutions are developed using homotopy analysis method (HAM) and for the numerical solutions the finite difference method in combination with an iterative scheme is used. A comparison between the analytical and the numerical solutions is presented. Moreover, the shear-thinning and shear-thickening behaviors of the non-Newtonian Sisko fluid are discussed through several graphs and a comparison is also made with the Newtonian fluid. (C) 2009 Elsevier Ltd. All rights reserved.