The aim of this study is to estimate the initial stress in reservoirs before production using 3D calibrated geomechanical models. We propose an inverse method for estimating stress. Wellbore data can be integrated in a Mechanical Earth Model in order to estimate stresses nearby wells. It yields a first rough estimation in the whole reservoir by a simple interpolation which is not in equilibrium with the external forces and boundary conditions. From this rough stress field, the inversion aims at finding a physically acceptable stress state (i.e.: in equilibrium with the external forces and boundary conditions) that fit the local stresses wells. The forward problem is ensured by a Finite Element Analysis which is able to take into account structures such as faults, which have a significant influence on the stress magnitude and orientation. Inverse loop stops when the stress computed near wells matches the one estimated using borehole data. The uncertainties on the boundary conditions, elastic parameters and the first stress estimation are taken into account with a stochastic approach. In this study, faults are built with a volumetric representation of the core and damage zone by introducing elastic parameters variations within. This representation is possible because only small deformations are expected.