1-3 piezoelectric composites are widely used as the transduction materials for underwater and ultrasonic transducers. In order to guide the design of the composite material and the devices based on it, a dynamic model is developed to precisely predict the dependence of the thickness drive on various parameters. For example, the velocity of the longitudinal wave, the dispersion curves of the wave propagation in 1-3 piezoelectric composite, and the antiresonance frequency, as well as the electromechanical coupling coefficient of the fundamental thickness mode, can be exactly predicted. The effect of the loss of the polymer phase on the properties of the 1-3 piezoelectric composite is also included in this theory; as a consequence, the quality factor of the 1-3 piezoelectric composite and its dispersion can be described. The origin of the lateral modes in the 1-3 composite plate can also be elucidated from this model, which shows quite different behavior from the early models such as the stop-band edge resonance model. Parallel to the analytic model, a systematic experimental study was also conducted to examine the mode coupling and the mode evolution with the thickness of a 1-3 composite plate.