Periodic composite ultrasonic transducers offer many advantages but the periodic pillar architecture can give rise to unwanted modes of vibration which interfere with the piston like motion of the fundamental thickness mode. In this paper, viscoelastic loss is incorporated into a three-dimensional plane wave expansion model (PWE) of these transducers. A comparison with experimental and finite element data is conducted and a design to damp out these lateral modes is investigated. Scaling and regularisation techniques are introduced to the PWE method to reduce ill-conditioning in the large matrices which can arise. The identification of the modes of vibration is aided by examining profiles of the displacements, electrical potential and Poynting vector. The dispersive behaviour of a 2-2 composite transducer with high shear attenuation in the passive phase is examined. The model shows that the use of a high shear attenuation filler material improves the frequency band gap surrounding the fundamental thickness mode.