  Inside neutron stars, the hadron-quark mixed phase is expected during the
first order phase transition from the hadron phase to the quark phase. The
geometrical structure of the mixed phase strongly depends on the surface
tension at the hadron-quark interface. We evaluate the shear modulus which is
one of the specific properties of the hadron-quark mixed phase. As an
application, we study shear oscillations due to the hadron-quark mixed phase in
neutron stars. We find that the frequencies of shear oscillations depend
strongly on the surface tension; with a fixed stellar mass, the fundamental
frequencies are almost proportional to the surface tension. Thus, one can
estimate the value of surface tension via the observation of stellar
oscillations with the help of the information on the stellar mass.
