Analysis of piezoelectric ultrasonic transducers implies a solution of a boundary value problem, for a boay which consists of different materials, including a piezoelectric part. The problem is dynamic at frequencies, where a typical wavelength is somewhat less than the size of the body. Radiation losses as well as internal losses may be important. Due to the complexity of the problem, a closed form solution is the exception rather than the rule. For this reason, it is necessary to use approximate methods for the analysis.Equivalent circuits, the Rayieigh-Ritz method, Mindlin plate theory and in particular the finite element method are considered. The finite element method is utilized for analysis of axisymmetric transducers. An explicit, fully piezoelectric, triangular ring element, with linear variations in displacememnt and electric potential is given. The influence of a fluid half-space is also given, in the form of a complex stiffness matrix. A special stacking procedure, for analysis of the backing has been developed. This procedure gives a saving, which is similar to that of the fast fourier transform algorithm, and is also wellsuited for analysis of finite and infinite waveguides. Results optained by the finite element method are shown and compared with measurements and exact solutions. Good agreement is obtained. It is concluded that the finite element method can be a valueable tool in analysis and design of ultrasonic transducers. Thesis submitted in partial fulfilment of the requirements for the Lic.Techn. degree at the Technical University of Denmark.