  The behavior of the shear modulus caused by proliferation of dipoles of
non-singular screw dislocations with finite-sized core is considered. The
representation of two-dimensional Coulomb gas with smoothed-out coupling is
used, and the stress-stress correlation function is calculated. A convolution
integral expressed in terms of the modified Bessel function $K_0$ is derived in
order to obtain the shear modulus in approximation of interacting dipoles.
Implications are demonstrated for the shear modulus near the melting transition
which are due to the singularityless character of the dislocations.
