The elasticity of neutron star crust is important for adequate interpretation
of observations. To describe elastic properties one should rely on theoretical
models. The most widely used is Coulomb crystal model (system of point-like
charges on neutralizing uniform background), in some works it is corrected for
electron screening. These models neglect finite size of nuclei. This
approximation is well justified except for the innermost crustal layers, where
nuclei size becomes comparable with the inter-nuclear spacing. Still, even in
those dense layers it seems reasonable to apply the Coulomb crystal result, if
one assumes that nuclei are spherically symmetric: Coulomb interaction between
them should be the same as interaction between point-like charges. This
argument is indeed correct, however, as we point here, shear of crustal lattice
generates (microscopic) quadrupole electrostatic potential in a vicinity of
lattice cites, which induces deformation on the nuclei. We analyze this problem
analytically within compressible liquid drop model, using ionic spheroid model
(which is generalization of well known ion sphere model). In particular, for
ground state crust composition the effective shear modulus is reduced for a
factor of $1-{u}^{5/3}/(2+3{\textstyle \phantom{\rule{0.167em}{0ex}}}u-4{\textstyle \phantom{\rule{0.167em}{0ex}}}{u}^{1/3})$ , where u is the filling factor (ratio
of the nuclei volume to the volume of the cell). This result is universal and
does not depend on the applied nucleon interaction model. For the innermost
layers of inner crust u~0.2 leading to reduction of the shear modulus by ~25%,
which can be important for correct interpretation of quasi-periodic
oscillations in the tails of magnetar flares.