The stress rupture strength of silicon carbide fiber-reinforced silicon carbide (SiC/SiC) composites with a boron nitride (BN) fiber coating decreases with time within the intermediate temperature range of 700–950°C. Various theories have been proposed to explain the cause of the time-dependent stress rupture strength. The objective of this paper is to investigate the relative significance of the various theories for the time-dependent strength of SiC/SiC composites. This is achieved through the development of a numerically-based progressive failure analysis routine and through the application of the routine to simulate the composite stress rupture tests. The progressive failure routine is a time-marching routine with an iterative loop between a probability of fiber survival equation and a force equilibrium equation within each time step. Failure of the composite is assumed to initiate near a matrix crack and the progression of fiber failures occurs by global load sharing. The probability of survival equation is derived from consideration of the strength of ceramic fibers with randomly occurring and slow growing flaws as well as the mechanical interaction between the fibers and matrix near a matrix crack. The force equilibrium equation follows from the global load sharing presumption. The results of progressive failure analyses of the composite tests suggest that the relationship between time and stress-rupture strength is attributed almost entirely to the slow flaw growth within the fibers. Although other mechanisms may be present, they appear to have only a minor influence on the observed time-dependent behavior.