This research program addresses the prevalent issues of failure computation with particular emphasis on material nonlinearities. The main focus will be on moving discontinuities either as localized shear bands or as macroscopic fractures. Three primary areas are: Development of "Moving Grid Techniques" to trace the formation of discontinuities that emerge from material failure, Formulation and incorporation of on-line "Interactive Graphics", Computational simulation of mesomechanical failure (progressive damage of internal material structure), macroscopic fracture (cracking of a full-scale prototype). Reliable failure predictions are among the most pressing issues related to accurate safety prediction of new and existing structures. In fact, questions such as maximum collapse load and the underlying failure mechanism require robust algorithm to predict. This research project will develop the necessary algorithm to resolve the failure mechanism(s) and at the same time follow the collapse of the structure.