The flow past a square cylinder at a high Reynolds number has been simulated through direct calculations and through the calculations using turbulence models. The present investigation highlights significant differences between the two approaches in terms of instantaneous flow, Strouhal number and the aerodynamic forces. The time-averaged drag coefficient and the rms fluctuations due to the direct calculation are higher than those due to the turbulence model. However, Strouhal number is underpredicted in direct calculations. The effect of shear on the flow has also been determined using the turbulence model. The time-averaged drag coefficient is found to decrease with the increase in shear parameter up to a certain value. Then it increases with the further increase in the shear parameter. On the other hand, the lift coefficient increases with the increase in shear parameter. Strouhal number shows a decreasing trend with the increase in shear parameter whereas the rms values of the drag and lift coefficients increase with the shear parameter. Kármán Vortex Street, mainly comprising of clockwise vortices due to shear, decays slowly compared to uniform flow condition.