It is known that rotation affects the turbulence structure substantially, and a knowledge of this effect is essential for improving the prediction of turbulent flows over rotating bodies. The extension of the κ-ε model for computation of rotating turbulent shear flows was carried out by introducing variable coefficients, $C_ε2$ and $C_μ$, in the turbulent dissipation rate equation and the eddy viscosity model, respectively. Special attention was given to capture the essence of the physics of rotating flows with the minimum amount of complexity and to improve the numerical convergency for easy use. When the proposed variable coefficients were applied to high Reynolds number standard κ-ε model, the augmentation of turbulent transport on the pressure surface of the channel and its damping on the suction surface seemed to be well captured by the computations provided the flow near the suction surface remains turbulent, while a low Reynolds number κ-ε model with the proposed $C_ε2$ and $C_μ$ yields predictions which are only in qualitative agreement with D.N.S. data of a rotating channel flow.