We present a new parallel numerical technique to estimate the effective elastic parameters of a rock core sample from threedimensional Computed Tomography (CT) images. Our method is based on the energy equivalence principle and a new approach to solve 3D static elasticity problem by iterative relaxation technique. We determine the elastic moduli by the parallel computation of potential energy of the elastic deformations arising in the sample under some homogeneous strains applied to the boundary thus simulating effects occurring in laboratory measurements. The obtained numerical results are discussed. The proposed method is verified using homogeneous samples with specified properties as well as for layered materials with effective parameters obtained according to the Schoenberg method. The effective parameters of a real carbonate core sample obtained from 3D CT-image are presented.