Resistance tube closure welds, referred to as pinch welds, are used to reliably seal small stainless steel tubing [1]. The quality of the bond is dependent upon, among other factors, the cleanliness of the tube bore. Post weld inspections are therefore desired as process control procedures. In previous studies, ultrasonics was shown to have considerable promise in this application. Thomas et al. [1] demonstrated that pattern recognition algorithms could be applied to the ultrasonic signals transmitted through the tubes to produce a correct classification of good and bad welds in several different sets of samples. The algorithms were somewhat dependent on the material from which the samples were fabricated, but all showed a good deal of commonality. In a parallel study, Rehbein et al. [2] examined, from a more mechanistic point of view, sets of tubes fabricated at the same time. They observed that gross disbonds could be easily detected from changes in signals either reflected from or transmitted through the bond line. When such disbonds were not present, they observed that signals doubly transmitted through the interface (i.e., the back surface echo) showed a trend to lower values as the bond quality decreased. This paper describes the sequel to that study, having the objective of developing a quantitative understanding of the interaction of the ultrasound with the pinch welds.