The hydrostatic approximation, which can be formally derived as small aspect ratio (the ratio of the vertical scale to the horizontal scale) limit, is a fundamental assumption in the geophysics and in particular for the large scale ocean and atmospheric dynamics. In spite of its importance and believed to be accurate in the geophysics, the rigorous justification is only proved before in the framework of weak solutions. In this talk we provide a justification of the hydrostatic approximation in the frameworks of both strong solutions and $z$-weak solutions and at the same time get the convergence rate. Both the isotropic case (that is with viscosities in all directions) and anisotropic cases (with viscosities in the horizontal directions only) will be considered.