We present an alternative method for treating numerically a problem of viscous flow with a boundary layer that is based upon regularization of the Navier-Stokes equations. Shishkin (1997) showed that grid methods perform poorly in dealing with the boundary layer. Traditional grid methods give poor agreement with the experimental data for high Re number flows. Shishkin showed that the remedy for these difficulties is the construction of special meshes in boundary layer. We present an alternative approach that is more efficient and less mesh dependent. Our approach is based upon the regularization of the Navier-Stokes equations, and we discuss the mathematical and physical aspects of this approach. Numerical results that we obtained by our regularization process in 2D and 3D are compared with the experimental measurements. We compared our model against : (1) The 3D driven cavity flow by Koseff and Street (1982) at Re = 3200 and 10;000; (2) a 2D backward facing step flow by Kim et al. (19..