Incompressible linear shear flow across a square cylinder is numerically analyzed by solving unsteady 2-D Navier-Stokes equations. Simulations are carried out for three sets of shear parameters, 0.0, 0.1 and 0.2 and two sets of solid blockage ratios, 6.25% and 10%. The aim of the present simulations is to find out the influence of shear on the onset of periodic time dependent flow, which is observed using time varying lift coefficient. With increasing shear, the critical Reynolds number, at which flow becomes time dependent, is reduced. The mean drag coefficient decreases either with increasing shear for a particular Reynolds number or with increasing Reynolds number for a particular shear parameter. © 2008 Elsevier Inc. All rights reserved.