We have incorporated the oblate distortion of the shape of the star due to the stellar rotation, which modifies the finite disk correction factor (fD) in the m-CAK hydrodynamical model. We implement a simplified version for the fD allowing us to solve numerically the non–linear m-CAK momentum equation. We solve this model for a classical Be star in the polar and equatorial directions. The star's oblateness modifies the polar wind, which is now much faster than the spherical one, mainly because the wind receives radiation from a larger (than the spherical) stellar surface. In the equatorial direction we obtain slow solutions, which are even slower and denser than the spherical ones. For the case when the stellar rotational velocity is about the critical velocity, the most remarkable result of our calculations is that the density contrast between the equatorial density and the polar one, is about 100. This result could explain a long-standing problem on Be stars.