One of the most interesting developments in engineering analysis during the last few years has been the rapid growth of boundary element methods. The first and second international conferences on this topic held in 1978 and 1980 attracted approximately 30 papers each, most of them from a few well known groups around the world. The third meeting in 1981, produced instead approximately 40 papers, many of them from young investigators working in newly created research groups. They have been attracted to boundary elements by the many advantages of the technique and were able to assimilate rapidly, the new ideas unencumbered by previous con­ ceptions. That third conference held in 1981 constituted in many ways a turning point for boundary elements and it indicated for the first time a general awareness of the industry to the research being carried out in the new technique. Engineering firms started to appreciate the advantages of the method mainly from the computa­ tional aided engineering point of view. The advantages of simple data input and output was rapidly understood by those professional engineers who were forced up to them to use cumbersome finite element codes. Boundary element practitioners in close contacts with the industry started to perceive that the method was gather­ ing a critical momentum of its own. This is now more evident by the diversity and quality of the papers in this volume, which are the edited Proceedings of the 4th International Conference, held at the University of Southampton in September 1982.