Dispersion of flexural waves in a compound solid cylinder containing a shear-spring-type imperfection between its constituents is investigated utilizing the three-dimensional equations and relations of the linear theory of elastodynamics. Attention is focused on the influence of the imperfection on dispersion curves. By using an analytical solution of corresponding field equations, dispersion equations for the cases considered are obtained. Based on numerical solutions of the equations, dispersion curves are constructed for a bi-material cylinder, consisting of steel and aluminum cylinders, for the first fundamental vibration mode. In particular, it is established that the type of imperfect contact conditions considered can give rise to additional branches of dispersion curve related to the fundamental mode. One of these branches approaches the dispersion curve obtained for a perfect interfacial contact, but the other disappears as the values shear-spring parameters decrease.