This paper reports the numerical calculations of uniform turbulent shear flow around a square cylinder. The predictions are obtained by solving the two-dimensional unsteady Navier-Stokes equations in a finite volume technique. The turbulent fluctuations are simulated by the standard $k-{varepsilon}$ model and one of its variant which takes care of the realizability constraint in order to suppress the excessive generation of turbulence in a stagnation condition. It has been found that the Strouhal number and the mean drag coefficient are almost unaffected by the shear parameter but the mean lift coefficient is increased. The present predictions are compared with available experimental data.