This paper presents a method for solving wave propagation problems of an infinite bar of arbitrary cross section with a circular cylindrical cavity. In the analysis the exact solution of the wave equations based on the three‐dimensional theory of elasticity which satisfies the boundary conditions of the inner circular cylindrical cavity has been utilized. The boundary conditions of the outer arbitrarily shaped surface of the bar are satisfied by use of the Fourier expansion collocation method. The analysis derives the frequency equation for determining the phase velocities of the bar of arbitrary cross section with the cavity. As an example numerical calculations have been carried out for an elliptical cross‐section bar with a circular cylindrical cavity.