Polymer matrix composites are seeing increasing use in structural systems (e.g. ships, bridges) and require a quantitative basis for describing their performance under combined mechanical load and fire. Although much work has been performed to characterize the flammability, fire resistance and toxicity of these composite systems, an understanding of the structural response of sandwich type structures and laminate panels under combined mechanical and thermal loads (simulating fire conditions) is still largely unavailable. Therefore a research effort to develop a model to describe the structural response of these glass/vinyl esters systems under fire loading conditions is relevant to the continuing and future application of polymer matrix composites aboard naval ships. The main goal of the effort presented here is to develop analytical models and finite element analysis methods and tools to predict limit states such as local compression failures due to micro-buckling, residual strength and times to failure for composite laminates at temperatures in the vicinity of the glass transition where failure is controlled by viscoelastic effects. Given the importance of compression loading to a structure subject to fire exposure, the goals of this work are succinctly stated as the:(a)Characterization of the non-linear viscoelastic and viscoplastic response of the E-glass/vinyl ester composite above Tg. (b)Description of the laminate compression mechanics as a function of stress and temperature including viscoelasticity.(c)Viscoelastic stress analysis of a laminated panel ([0/+45/90/-45/0]S) using classical lamination theory (CLT). Three manuscripts constitute this dissertation which is representative of the three steps listed above. First, a detailed characterization of the nonlinear thermoviscoelastic response of Vetrotex 324/Derakane 510A - 40 through Tg was conducted using the Time - Temperature - Stress - Superposition Principle (TTSSP) and Zapas - Crissman model. Second, the modeling approach and viscoelastic relaxation mechanism is validated by substituting the shear relaxation modulus into a compression strength model to predict lifetimes for isothermal and one sided heating of unidirectional laminates. Finally, viscoelastic stress analysis using CLT is performed for a general laminated panel to predict lifetimes under one sided heating. Results indicate that when temperatures remain in the vicinity of Tg, the laminate behavior is controlled by thermoviscoelasticity. / Ph. D.