This work presents a new formulation of the Boundary Element Method (BEM) for nonlinear time-dependent problems. An incremental process, in order to reach the steady state condition and the secondary steady stage for visco-plasticity and creep respectively, has also been developed. This research includes the development of a new Boundary Element Formulation for analysis of fracture problems related to visco-plasticity and creep. For the visco-plastic and creep crack analysis the Dual Boundary Element Method, (DBEM) is formulated. The implementation of visco-plasticity and creep in the formulation is taken into account by domain integrals in both boundary integral equations. The creep analysis is basically applied to metals, and this is confined to standard power law creep equations. Constant applied loads are used to demonstrate time and strain hardening effects. The calculation of the modified fracture parameter J-Integral, which is called C(t)-Integral for creep analysis, is obtained by applying this method to crack problems. This book is appropriate for researchers, Ph.D. and postgraduate students involved in modern numerical methods and non-linear analysis.