This report provides a summary of the Elastic-Plastic Finite Element Alternating Method (EPFEAM), the T* -integral fracture mechanics parameter, and the use of both tools to predict the residual strength of aircraft panels with multiple-site damage. Because this report is meant to be self-contained and each of the three subjects is a considerable research topic in itself, the report is written in three parts. Part I, EPFEAM Theory provides a summary of the elastic-plastic finite element alternating method (EPFEAM) and the algorithms for fracture analysis and crack growth predictions. Part II, Fracture and the T*-Integral Parameter provides a complete description of the T*-integral fracture parameter including a detailed discussion of the theoretical basis of T* and the practical aspects of its use for fracture predictions. Finally, Part III, Computational Predictions of the NIST Multiple Site Damage Experimental Results provides a series of predictions of a number of fracture tests performed at the National Institute of Standards and Technology (NIST). These predictions are then compared with the experimental data, thus validating the present model for computing the residual strength under wide-spread-fatigue damage conditions. The reader that is interested in all the topics can study all the three self-contained parts, while the reader that is only interested in the practical aspects of fracture predictions using these methods can read only Part III. This is the Part I report, EPFEAM Theory.