Stress rupture is a catastrophic failure mode in continuous unidirectional fiber composites, such as those used in composite overwrapped pressure vessels (COPVs). COPVs are currently used mainly in aerospace applications, such as storing the reserve oxygen on the International Space Station. Indeed a carbon/epoxy COPV failure caused the September 2016 explosion of the SpaceX Falcon 9 rocket at Cape Canaveral, leading to more than a billion dollars of damage. Currently COPVs are used in relatively small numbers, but the day is rapidly approaching when they will be used in the millions in many aspects of daily life, particularly in automotive applications. My research seeks to better understand stress rupture and more accurately estimate the probability that a specific composite structure will fail in stress rupture. Prediction of a composite’s stress rupture behavior is heavily based on results from extensive testing, as there are not yet methods to predict a composite’s stress rupture behavior based on the component materials’ properties. Testing results in comparatively small datasets of accelerated test data, which then must be extrapolated to predict a failure probability for a the service life of interest. This dissertation shows that the method used to analyze these datasets is crucial to accurately estimating the probability of a stress rupture failure, and also presents a data analysis method with lower variance and MSE estimates than current ad-hoc industry methods. Furthermore this dissertation compares current stress rupture models and derives a new, micromechanical stochastic stress rupture model.