Piezoelectric actuators are widely used for the nano/micro positioning and adjustment systems. In the paper, the investigation on the oscillations of contacting surfaces of the piezoelectric thick-walled cylinder is presented. Piezoelectric cylinder is the main component of piezomechanical system named as piezo-screw and is used to turn the screw. This investigated piezomechanical system can be used for the precise positioning with a high resolution (less than 50 nanometers). Piezoelectric cylinder has radial polarization. Traveling-wave oscillations of the second circumferential modal shape (n = 2, m = 1) are excited. Three different electrode topologies are used to drive the screw. Electrodes are grouped into upper and low groups in both topology cases. Each group consists of six electrodes where positions of corresponding electrodes in upper and lower group are shifted by π/6. Numerical investigation of the traveling wave oscillation is performed and dependencies oscillation trajectories of contact surfaces on excitation schemes are determined when three different electrode topologies are used. Dependency of oscillations of contacting points upon length of the actuator is analyzed as well. Advantages and disadvantages of each excitation case are discussed.