The evolution of matrix cracking, degradation of mechanical properties, and distribution of fatigue life of a SiC fiber-reinforced orthorhombic titanium aluminide (Ti-22Al-23Nb) composite under various applied cyclic stresses were analyzed by computer simulation. The propagation of matrix cracks was modeled by a modified fiber-bridging model which incorporates the effect of fiber breakage on crack growth. The residual stiffness was then predicted by using the shear-lag model, and the post-fatigue tensile strength was predicted by using the residual load-carrying capacity of the fatigued composites as the failure criterion. Finally, the distribution of fatigue lives was predicted according to various fiber strength distributions simulated by a random number generator. The simulated matrix crack propagation rates, residual stiffness, residual tensile strength and fatigue life are correlated with experimental results.