This book provides a better understanding of the theories associated with finite element models of elastic and viscoelastic response of polymers and polymer composites. It covers computational modeling and life-prediction of polymers and polymeric composites in aggressive environments. It begins with a review of mathematical preliminaries, equations of anisotropic elasticity, and then presents finite element analysis of viscoelasticity and the diffusion process in polymers and polymeric composites. The book provides a reference for engineers and scientists and can be used as a textbook in graduate courses.