Inversion layer ultrasonic transducers have been investigated recently as an interesting approach in wideband transducer design. In this paper we present an analytical model of multilayer ultrasonic transducers with an inversion layer. Our analysis of the wave propagation problem of an inversion layer transducer includes a functional decomposition of the electrical input impedance. It becomes clear from this decomposition that an inversion layer transducer can be modeled as three elements in series connection, i.e., a clamped capacitance, a classical motional impedance, and a coupled motional impedance. The first two elements make up the classical model of a single element transducer. The coupled motional impedance describes the coupled interaction between the regular and the inverted piezoelectric sublayers, and thus reflects the effect of an inversion layer. We present examples which show that inversion layer transducers are advantageous in achieving such useful features as dual-frequency operation mode as used in harmonic imaging or broadband performance desired in most ultrasonic applications.