This paper is concerned with wave propagation in elastic rods of cross–sectional shapes that admit coupling between bending and torsional motions. Dispersion relations for progressive and evanescent waves are presented in closed form. The general case of triple coupling and the special case of double coupling are considered. The propagation characteristics are analytically presented in the limits of the long and the short waves. Waveguide modes in these limits are presented as asymptotic expansions. The polarization behaviour in various regimes of propagation is studied. Eigenvalue veering is observed for coupled modes. For the complete spectrum involving complex wavenumber, the problem of obtaining the dispersion relation and the propagation modes is cast as a standard eigenproblem. Illustrative examples are given.