Fiber bundles and unidirectional (UD) continuous fiber composites are used in a variety of applications, including in composite overwrapped pressure vessels (COPVs) and bulletproof vests. 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, and in 2003 a police officer was fatally shot by a bullet that went through his vest. While the probability of these types of failures is low, each carries a large monetary and/or human cost. Furthermore, full sized specimens can be costly to test. For body armor the long term reliability is largely a function of material ageing, degrading the mechanical properties. The susceptibility of body armor to ageing is highly dependent on both the type of material and the conditions it is exposed to. In contrast, COPVs can effectively degrade with no further cause than a constant, low level pressure. The high stakes, low probability nature of these failures makes failure prediction a challenging and interesting research problem, requiring a unique blend of experiments with both statistical simulations and theoretical modeling. The broad goal of my work is to develop and verify a stochastic Monte-Carlo simulation to predict the stress strain behavior, at the lower probability tail, for bulk composite materials and understand how this behavior changes over time.Fiber bundles and unidirectional (UD) continuous fiber composites are used in a variety of applications, including in composite overwrapped pressure vessels (COPVs) and bulletproof vests. 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, and in 2003 a police officer was fatally shot by a bullet that went through his vest. While the probability of these types of failures is low, each carries a large monetary and/or human cost. Furthermore, full sized specimens can be costly to test. For body armor the long term reliability is largely a function of material ageing, degrading the mechanical properties. The susceptibility of body armor to ageing is highly dependent on both the type of material and the conditions it is exposed to. In contrast, COPVs can effectively degrade with no further cause than a constant, low level pressure. The high stakes, low probability nature of these failures makes failure prediction a challenging and interesting research problem, requiring a unique blend of experiments with both statistical simulations and theoretical modeling. The broad goal of my work is to develop and verify a stochastic Monte-Carlo simulation to predict the stress strain behavior, at the lower probability tail, for bulk composite materials and understand how this behavior changes over time.