Stress rupture is a sudden, stochastic failure mode that occurs in continuous unidirectional fiber composites and in particular composite overwrapped pressure vessels subject to long-term, steady loads. A common approach for modeling stress rupture is the probabilistic classic power-law model for material breakdown within a Weibull framework (CPL-W). This model includes a number of parameters, which need to be estimated from real data. These parameters may be estimated in a variety of different ways. This paper investigates how best to estimate the parameters of the CPL-W model given a set of experimental data for both composite strength and composite lifetime obtained at multiple stress levels. Eight different maximum likelihood estimation approaches are investigated regarding their differing errors of estimation. The accuracy of each method is estimated by repeated Monte Carlo simulations of specific instances of the CPL-W model typical of various carbon/epoxy and aramid/epoxy fiber composite systems; no actual experimental data are analyzed. One particular approach stands out as having the least estimation error while a commonly used approach does very poorly.