Identification of elastic constants of three-dimensional anisotropic materials is much more complicated than the corresponding one in two-dimensional materials. This is because of the increased number of the elastic constants in three-dimensional materials. In this paper, an inverse method for determination of elastic constants of three-dimensional orthotropic, monoclinic and anisotropic materials using elastostatic measurements is presented. Strain measurements at some sampling points obtained from several elastostatic experiments are considered as the elastic response of the material. The solution is based on minimization of the difference between measured strains and the corresponding calculated ones at sampling points. The finite element method is used for sensitivity analysis, while the Tikhonov regularization method is used for stablizing the solution. Designing a single elastostatic experiment in which all of the material parameters affect the response distinctively is very difficult and seems impossible. By using the data obtained from a few different experiments, we are able to collect enough information to reach a stable and accurate solution. In the present research, 9 constants of orthotropic materials, 13 constants of monoclinic materials and 21 constants of anisotropic materials have been successfully identified. Effects of different parameters on accuracy and efficiency of the proposed method are studied by presenting several numerical examples.