In recent years, bridge foundations have been in the spotlight throughout the nation. Bridges built over running water are susceptible to erosion or scour around their foundations. The reduction in load capacity to piers and abutments pose a safety risk to highway motorists. It has become necessary for engineers to examine and monitor these "scour critical" bridges. The difficulty arises with subsurface foundations of which very little is known about their construction. Hence, the methods applied to analyzing "Unknown Foundations" have become a necessary topic of research. This thesis explores a method to determine foundation lengths. Similar to Sonic Echo / Impulse Response, this procedure measures reflected shock waves sent through concrete pilings. The technique is non-destructive in nature and is performed near the surface of the foundation. The test is performed on the side of the exposed piling. Current methods are limited by the fact that the tops of most pilings are inaccessible due to pilecaps or beams. Often times, pilings are embedded in stiff soils, which have a dampening effect on the stress waves. This thesis employs a method of analysis that will overcome such limitations and provide engineers with another tool to determine subsurface foundation lengths.