Tapered-thickness piezoelectric ceramics have been used in novel devices and imaging techniques, such as wideband transducers and frequency-controlled acoustic-beam translation. However, further application requires an adequate theoretical model of these tapered ceramics. In this work a staircase model is developed in which the thickness gradient is represented as discrete steps. Each step is modeled as an independent, constant-thickness section which contributes to the net response. The theoretical electric input impedance, spectral content, pulse, and continuous-wave pressure profile responses obtained with the model are shown to be in close agreement with the measured response of a tapered piezoelectric transducer.