This volume covers the proceedings of the workshop sponsored by the Institute for Computer Applications in Science and Engineering ((CASE) held 28-30 July 1988 in Hampton, Virginia, at the NASA Langley Research Center. It consists of 13 articles by finite element researchers and practitioners and 13 intended to assess the impact of the theory on practice and to suggest areas of future research. About one-half of the articles review the theoretical aspects of the finite element method while the remaining are devoted to advanced applications where research is still required.