Flexible ultrasonic waveguides are widely used in minimally invasive surgery. Their design is sophisticated procedure because they exhibit complex vibration phenomena like parametric resonance and intermodal interactions and at present there are no scientific and engineering theories capable to facilitate this procedure. This work presents generic mathematical and computer models which may be useful for design of flexible waveguides. Timoshenko’s model and Webster’s equation are used to study resonant conditions for flexural and longitudinal vibrations and to obtain their graphical representation in the form of resonant curves and surfaces depending on the number of varied parameters. Correctness of the proposed models is verified by means of finite elements method.