The aim of this paper is to define a linear model of a planar standing wave ultrasonic motor (SWUM). First, the analytical approach using the variational formulation is presented. An identification method is deduced to find the parameters of a vibrating rectangular plate. Non-linearities are also emphasized and verified by the experimental measurements. Secondly, the mechanical energy conversion of the actuator is identified, using an average behavior modelling and a linear approach for the contact interaction. Finally, a complete modelling of the actuator is presented, using the Causal Ordering Graph formalism.