The transition of square cylinder wake flow from two-dimensional (2-D) to three-dimensional (3-D) when inflow is subjected to linear shear is examined numerically. The value of the non-dimensional shear parameter (K) considered in this study are 0.0, 0.1, and 0.2. The range of Reynolds number (Re) defined based on the centerline velocity and cylinder width is from Re = 150 to 700. The transition of the wake flow from 2-D laminar to 3-D is marked by streamwise vortical structures. Unlike in uniform flow, in shear flow the transition is characterized by single mode of spanwise wavelength. The critical Reynolds number (Recrit), at which the transition from 2-D to 3-D occurs, is less in case of shear flow. The magnitude of the mean lift coefficient increases with increasing shear parameter on the positive side. The strength of the Karman vortices on the top side is higher and on the bottom side is lower when compared with the same in the uniform flow. © 2010 John Wiley & Sons, Ltd.