This volume presents the proceedings of the First International workshop on Parallel Scientific Computing, PARA '94, held in Lyngby, Denmark in June 1994. It reports interdisciplinary work done by mathematicians, scientists and engineers working on large-scale computational problems in discussion with computer science specialists in the field of parallel methods and the efficient exploitation of modern high-performance computing resources. The 53 full refereed papers provide a wealth of new results: an up-to-date overview on high-speed computing facilities, including different parallel and vector computers as well as workstation clusters, is given and the most important numerical algorithms, with a certain emphasis on computational linear algebra, are investigated.