A finite volume technique is presented for the numerical solution of steady laminar flow of Oldroyd-B fluid in a lid-driven square cavity over a wide range of Reynolds and Weissenberg numbers. Second order central difference (CD) scheme is used for the convection part of the momentum equation while first order upwind approximation is employed to handle viscoelastic stresses. A non-uniform collocated grid system is used. Momentum interpolation method (MIM) is used to evaluate face velocity. Coupled mass and momentum conservation equations are solved through iterative SIMPLE (serni-implicit method for pressure-linked equation) algorithm. Detailed investigation of the flow field is carried out in terms of velocity and stress fields. Differences between the behavior of Newtonian and viscoelastic fluids, such as the normal stress effects and secondary eddy formations, are highlighted. (C) 2009 Elsevier B.V. All rights reserved.