Abstract In this paper we discuss the non-linear contact problem between the stator and the rotor of an ultrasonic travelling were motor. For a first simplified mathematical model the problem is formulated for a linear motor in which the stator is modelled as a Bernoulli-Euler beam and the slider (rotor) is assumed to be rigid. A thin layer of visco-elastic material is assumed to exist between stator and slider. Expressions are obtained for the contact pressure between the two parts. The frictional forces both in the sticking and in the sliding zone can then be easily obtained assuming Coulomb friction.