  Neutron stars are the densest objects in the Universe. They have
microscopically homogeneous core and heterogeneous crust. In particular, there
may be a specific layer inside neutron stars, the mantle, which consists of
substantially non-spherical nuclei immersed in a background of relativistic
degenerate electrons and quasi-free neutrons. In this paper we reconsider
transverse shear modulus for cylindrical phases of the mantle within the
framework of compressible liquid drop model. We demonstrate that transverse
shear affects the shape of nuclear clusters: their cross-section becomes
elliptical. This effect reduces respective elastic constant. Using a simple
model we perform all derivations analytically and obtain the expression for the
transverse shear modulus, which can be useful for astrophysical applications.
