This conference was the sequel to the Third International Conference on Computational Stochastic Mechanics which was held on the island of Santorini (Thera), Greece on June 14-17, 1998. The aim of these meetings is to provide a forum for exchanging ideas on the status of computational methods applied to stochastic mechanics, and for identifying needs for further research. The conference covered both theoretical concepts and practical applications. The papers of this volume address themes on Linear and Nonlinear Random Vibration; Safety and Reliability; Structural Identification and Control; Random Processes and Fields; Earthquake Engineering; Wind Engineering; Offshore Engineering; Insurance for Natural Hazards; Genetic Algorithm; and Dynamic Systems Modeling of the Stock Market. This volume will be of interest to researchers and practitioners using stochastic methods to solve a broad spectrum of problems in applied science and engineering.