In this talk, we talk about the hydrostatic approximation for the Navier-Stokes system in a thin domain. When the convex initial data with Gevrey regularity of optimal index 32 in x variable and Sobolev regularity in y variable, we justify the limit from the anisotropic Navier-Stokes system to the hydrostatic Navier-Stokes/Prandtl system. Due to our method in the paper is independent of ε, by the same argument, we also get the hydrostatic Navier-Stokes/Prandtl system is well posedness in the optimal Gevrey space.