The transient response of ultrasonic biomedical transducers and arrays is becoming increasingly important as a result of the wideband excitations which are currently envisaged for various biomedical applications. In the present paper, a computer model is developed to evaluate the transient transmit/receive response of multielement beam steered arrays of acoustically coupled piezoelectric thickness expander transducers. Each transducer is represented by a distributed parameter model which includes the effects of mechanical backing and matching materials. A set of coupled convolution integral equations are developed from the model to characterize the transient transmit/receive response of an army and scatterer configuration. These equations are an extended version of earlier work [P. Stepanishen, J. Acoust. Soc. Am.50, 964–974 (1971)] and can be readily solved using recursire techniques. Numerical results are presented to illustrate typical transient acoustic field and receive phenomena which result from the short pulse excitation of phased arrays of ultrasonic transducers in the MHz range of biomedical interest. [Work supported by NIH.]