- In this paper we present a stress-based least-squares finite-element formulation for the solution of the Navier-Stokes equations governing flows of viscous incompressible fluids. Stress components are introduced as independent variables to make the system first order. Continuity equation becomes an algebraic equation and is eliminated from the system with suitable modifications. The h and p convergence are verified using the exact solution of Kovasznay flow. Steady flow past a large circular cylinder in a channel is solved to test mass conservation. Transient flow over a backward-facing step problem is solved on several meshes. Results are compared with that obtained using vorticity-based first-order formulation for both benchmark problems. Copyright 2007 John Wiley & Sons, Ltd.