The optimization of piezoelectric ultrasonic transducers has tradisionally been done through trial and error, somewhat guided by one-dimentional simulations. This can often be a very time-consuming and expensive process, hence a more extensive simulation method is desired.A series of finite element models of piezoelectric ultrasonic transducer has been made in COMSOL Multiphysics. The initial models were designed to emulate the conditions assumed in a one-dimentional transducer model, and their validity could thus be confirmed by said model. Later models did not emulate these conditions, and a lossless model of a spherical disc with backing and a single matching layer was successfully implemented. Attemps had been made to include mechanical loss in the initial models, but was only partially achieved. All loss was thus excluded from later models. A final model with a piezoelectric layer poled in the radial direction was not successfully designed, as the varying poling direction proved to be difficult to implement.