Most are not aware that the first practical applications of stress wave simulations were based on the Method of Characteristics and were performed using graphical tools. Today these tools have been replaced by computers and the computer algorithm for the Method of Characteristics (MOC) is almost certainly the most commonly used algorithm for stress wave simulations, like driveability studies (both for impact hammers and vibratory hammers), signal matching (both to assess pile capacity and to perform pile shape analysis), the design of hammer parts, hammer cushions, and Rapid Load Testing simulations. This paper will be a sequel to the paper “Thirty Years of Experience with the wave equation solution based on the Method of Characteristics” that was presented at the Stress Wave Conference in Kuala Lumpur, 2004. As such it will provide an overview of the application of the method in foundation testing: from the early beginnings using the graphical methods to the current advanced driveability analyses. The overview will be illustrated by actual examples generated by the wave equation program AllWave that also demonstrate how the outcome of soil investigation testing is transformed into soil model parameters (incl. soil fatigue parameters) to ensure that the analysis generates reliable results.