In the context of shell theory in continuum mechanics, based on three-dimensional displacement fields and assuming height as a differentiable function of the geodetic surface coordinates analytical surface deformation theory provides a method for analyzing the contemporary state of surface deformation of the Earth's crust using differential geometry. In this method, based on finite elements representation of the Earth's crust (Delaunay triangulation) deformation analysis is based on a two-dimensional computational approach: Gaussian and mean curvatures are computed using metric tensor and the second fundamental form. Variations of the mean and Gaussian curvatures in Makran, 0.503×10-14/myr and 1.097×10-21/m2yr respectively, obtained from the Iran global GPS campaigns (epochs 2001 and 2005) are a signature for the subduction process in this area. Moreover, maximum change in the curvature are in accord with the main Zagros and Alborz (+1.574×10-21/m2yr and-9.992 ×10-21/m2yr ) folds in Iran. Frequently the subsidence paths in precise leveling network of Iran are in areas with reduction in curvature.