Recently, the artificial neural network has experienced a surge in popularity and is now one of the most rapidly expanding areas of research across many disciplines. The main reason is in its powerful and adaptive abilities to treat various complex problems. One can be sure that with its further developments, neural networks will strongly impact many conventional disciplines from the standpoint of methodology. In the field of mechanics, the research and application of both neural network and revolutionary computing are especially active and successful. The back propagated multilayered network is one of the main types applied to engineering. The related works concern almost all topics of engineering science and mechanics, such as, approximation of structural analysis, assessment of structural damage, fault diagnosis, prediction, strategic management, decision making, structural optimization, etc. The aim of this review is to summarize and recapitulate the up-to-date developments and applications of neural networks and computing in mechanics, with emphasis on the back propagation algorithm of multilayer networks. Not only are the fundamental principles outlined clearly, but some typical examples are also presented. It is hoped that this review article can promote the development and applications of neural network and computing in mechanics. This article contains 221 references.