1. General introduction and equations of solid mechanics -- 2. A review of the finite element method -- 3. Finite element models of linear viscoelastic materials -- 4. Finite element analysis of diffusion in polymer and polymer matrix composites -- 5. Finite element models of nonlinear viscoelastic materials -- 6. Finite element analysis of nonlinear diffusion in polymers -- 7. Non-Fickian solvent diffusion in a solid with large dilatation -- 8. A coupled hygrothermal cohesive layer model for simulating debond growth in bimaterial interfaces -- 9. A viscoelastic cohesive layer model for prediction of interlaminar shear strength of carbon/epoxy composites -- 10. A multi-scale viscoelastic cohesive layer model for predicting delamination in high temperature polymer composites.