A continuum-damage-mechanics-based model is proposed for the analysis of the progressive failure process in laminated composite structures. The laminate's response is determined by nonlinear constitutive equations that account for each type of matrix-dominated damage through strain-like internal state variables. Evolution of these internal state variables is governed by the damage-dependent ply-level stresses. The updated damage state and the ply-level stresses are then employed in the local-global evaluation of component failure. This model is incorporated into a finite-element analysis code to facilitate the examination of structures with spatially varying stress fields. The stress and damage distribution obtained from the analysis at various points in the loading history provide information about the progression of events leading to the failure of the component. The progressive failure of fatigue-loaded rectangular crossply-laminated plates containing a centered circular cutout has been examined with the model. Most of the predicted damage is localized in a region near the cutout. Rather than propagating outward, the damage intensifies in this region until failure occurs. The feasibility of modeling the evolution of each type of subcritical damage is demonstrated with the current framework. This ability to simulate the progressive failure process at this level of detail will assist in the design of safer and more efficient composite structures.