This study aims to estimate elastic properties as well as voids interaction energy within the context of 3D nano-porous materials exhibiting spherical or cylindrical voids, with or without the effect of surface energy. For this purpose, numerical homogenization is applied, based on the finite element method (FEM) in combination with the level-set technique. Surface energy is approximated by explicitly taking into account its contribution to overall stiffness in the variational formulation. Several cases are then investigated to appreciate the interaction energy between multiple 3D nanovoids on the actual behavior of nanomaterials. As expected, and like surface energy, the results show that interaction energy keeps affecting the effective behavior by increasing the size of RVE as well as the number of voids inside. This influence is more marked the more cylindrical the voids and the more closely they are adjacent to each other.