The flexural ultrasonic transducer is a robust and inexpensive device which can be used as either a transmitter or receiver of ultrasound, commonly used as proximity sensors or in industrial metrology systems. Their simple construction comprises a piezoelectric disc bonded to a metal cap, which is a membrane that can be considered as a constrained plate. Flexural transducers tend to be driven with a short voltage burst of several cycles at a nominal resonant frequency, in one of two vibration modes. The physics of their vibration response has not been thoroughly reported, and yet an understanding of their operation is essential to optimise application. The vibration behaviour of a flexural transducer can be discretised into three principal zones, comprising a build-up to steady-state, steady-state, and a natural decay, or ring-down. This discretisation can be used to develop mathematical interpretations of the flexural transducer response. Through a combination of experimental methods including laser Doppler vibrometry, and the development of a mechanical analog model, the response mechanisms of flexural transducers are investigated.