Conventional numerical methods like the Finite Element Method fail to be efficient to model the propagation of ultrasonic guided waves in real structures. The required fine mesh and the high number of degrees of freedom when solving the wave propagation problem in the time domain lead to a high computational effort and a need of big memory storage capacity. On the other hand, analytical and semi-analytical methods, which offer fast and accurate results, can be only applied to relatively special geometries. In this contribution the use of an hybrid of analytical and spectral methods to model the propagation of elastic guided waves in plates is studied. Guided wave propagation excited by bonded piezoelectric transducers is simulated with this approach. The piezoelectric transducers are modeled using spectral methods and the response of the plate is calculated using analytical methods. The mathematical modeling of the transducer-plate interface bonding conditions is presented. These conditions are subsequently discretized using an hybrid analytic-spectral formulation in the frequency domain. The numerical accuracy of the obtained results is verified by comparison with other numerical methods such as the finite element method.