This paper deals with the determination of stress evolution in bridging fibers during fatigue crack growth in a SM1240/Timetal-21S composite using the finite element method. Several parameters affecting this evolution were considered, namely, the process-induced residual stress, the creep characteristics of the matrix layer surrounding the fiber, the test temperature, and the loading frequency. In support of these calculations, a series of elevated temperature fatigue crack growth tests was conducted to identify the crack growth behavior of the composite when subjected to different temperatures at both high and low loading frequencies. Results of this numerical/experimental work were then utilized in conjunction with a postulated fiber fracture criterion based on the notion that a competition exists between the increase in the axial fiber stress and the continuous degradation of the fiber strength due to cyclic wear induced by the interface frictional shear stress. The conclusions of this study show that the axial stress in the bridging fibers increases with an increase in temperature and with a decrease in both the loading frequency and the matrix grain size. A combination of high-temperature, low-frequency, and small-matrix grain size would enhance creep deformation of the matrix, thus leading to an increase in the rate of the load transfer from the matrix to the bridging fibers. Furthermore, the presence of a compressive residual stress state in the bridging fibers retards the time-dependent increase of their axial stress. The fatigue strength of the bridging fibers was estimated to range from 720 to 870 MPa within the temperature range of 500 to 650°C. This strength was found to depend on both the temperature and the loading frequency.