Abstract: This talk aims at proposing an analysis of the mathematical and numerical modelling of ultrasonic piezoelectric sensors used in non destructive testing. This includes the well-posedness of the final model, the rigorous justification of the underlying approximation and the design and analysis of a numerical method. More precisely, a mathematical justification of the classical quasi-static approximation is presented, then particular attention is devoted to the different boundary conditions used to model the emission and reception regimes of the sensor. Finally, an energy preserving finite element / finite difference numerical scheme is presented as well as numerical results.