Exact solutions for flexural ridge wave propagation around a circular cylindrical tube have not previously been possible. Rather, such problem used to be solved numerically or using an empirical formula. This study investigates the dispersive properties of ridge waves traveling circumferentially around piezoelectric tubes, as well as their resonant modes. Based on the separation of variables, the displacements of ridge waves are represented as the product of a cross-sectional coordinate-dependent function and the propagator along the circumference of a tube. The dispersion equation of ridge waves is formulated by using Hamilton’s principle and the so-called bi-dimensional finite element method (Bi-d FEM). Furthermore, the dispersion curves of traveling waves and resonant frequencies corresponding to standing waves are solved numerically. Several applications, such as an optimal design for circular cylindrical ridge wave ultrasonic motors, are illustrated.