This paper deals with numerical computational techniques on viscous flows with free surface past a ship hull by using an improved Reynolds-Averaged Navier-Stokes solver with global conservation. In the first place, we used the two kinds of computational grids in order to improve the computing efficiency. After computing free surface of flows by coarser grid, we changed to detailed computation of viscous flows with free surface by finer grid. In the second place, the original Baldwin-Lomax turbulence model was modified by introducing the two kinds of turbulence modifications in order to obtain the simulation of stern flow such as the hook shape of axial velocity contours. These numerical computational techniques are applied to the simulation for viscous flows with free surface by a series 60 ship model. The numerical results are compared with measurement data and we show the usefulness of these numerical techniques and introducing of the modified Baldwin-Lomax turbulence model.