This article presents the main stages and challenges in modelling and designing of modern ultrasonic welding and cutting systems. First, the key components of such a system, such as an ultrasonic stack (con- sisting of a high power ultrasonic transducer and a sonotrode) and a digitally controlled ultrasonic power supply with precise control of the output power, have been considered. Next, a concept of measurement system for verification and validation of mathematical models of ultrasonic stacks and its components has been presented. Finally, a method of ultrasonic stack e-diagnosis based on ultrasonic transducer electrical impedance measurement during welding and cutting process has been described