This book contains the edited versions of most of the papers presented at the 9th international conference on boundary elements held at the university of stuttgart, germany from august 31st to september 4th, 1987, which was organized in co-operation with the computational mechanics institute and gamm (society for applied mathematics and mechanics). this conference, as the previous ones, aimed to review the latest developments in technique and theory and point out new advanced future trends. the emphasis of the meeting was on the engineering advances versus mathematical formulations, in an effort to consolidate the basis of many new applications. recently engineers have proposed different techniques to solve non-linear and time dependent problems and many of these formulations needed a better mathematical understanding. furthermore, new approximate formulations have been proposed for boundary elements which appeared to work in engineering practice, but did not have a proper theoretical background. the conference also discussed the engineering applications of the method and concentrated on a link between bem practitioners, industrial users and researchers working on the latest development of the method. the editors would like to express their appreciation and thanks to ms. liz newman and mr. h. schmitz for their unstinting work in the preparation of the conference.