Quality of the ultrasonic imaging depends on probing signal. Application of the spread spectrum (SS) signals offers significant advantage over conventional signals: higher signal-to-noise ratio can be achieved and spectral content can be programmed. Yet, such SS signals like chirp and coded sequences suffer for the sidelobes which are induced by compression processing. Arbitrary position and width pulse (APWP) trains is a new class of SS signals which are expected to maintain advantages of the square pulse and the SS signals. Usual approach of SS signals application does not assume signal optimization. The novelty of the APWP approach is the optimization of the APWP train accounting of the signal transmission through system. In order to speed up the optimization iterations, a mathematical model of the APWP signal transmission through ultrasonic system is needed: instead of doing the iterations in real environment, those can be accomplished mathematically, using the system transmission model in order to sustain the experiment conditions. The development of the transmission model of the system is presented; the models are compared using the correlation properties. The results of the investigation are presented.