A previously introduced method to study many-body electrostatic interactions among spherical particles [H. J. H. Clercx and G. Bossis, Phys. Rev. E 48, 2721 (1993)] has been used to study yield stresses and shear moduli for simple cubic (SC), simple hexagonal (SH), and body-centered tetragonal (BCT) structures, with polarizable spheres on the lattice sites, to gain insight in the electrostatic response of these structures to externally applied stresses. The shear modulus G and the static yield stress tau(s) have been calculated for several ratios of particle to fluid dielectric constant. It turned out that interchain interactions are very weak in SC and SH structures which is confirmed by the nearly linear cp dependence of G and tau(s) (even no weak maximum appears in these curves). The results reported for the BCT structure are rather unexpected, because both G and tau(s) suddenly decrease to zero at large volume fractions. We discuss the data for G and tau(s) and compare some of these results with data obtained by employing the dipolar approximation and the Laplacian relaxation technique to calculate the electrostatics. This comparison shows that in general a multipolar approach is indispensable in obtaining correct values for G and tau especially the dipolar approximation underestimates these quantities. As an example the strength of single vs double chains has been compared for both the dipolar approach and a multipolar calculation. In the dipolar approximation the double chain structure seems strongest. However, multipolar calculations show that the single chain structure is stronger than the double chain structure.