The design of commercial aircraft structures composed of composite materials requires the ability to predict failure loads in laminated shells containing cracks. A damage zone of considerable influence is known to develop in advance of the crack tip in a composite material. The objective of this investigation was to develop a computational model that simulates progressive damage growth around cracks and allows the prediction of failure loads in complex laminated shell structures. This was accomplished through the use of a relatively simple, nonlocal damage model that incorporates strain-softening. The model was implemented in a finite element shell program. An analysis was performed on a section of a composite aircraft fuselage containing a crack and subjected to internal pressure loading. Reasonably good agreement was found between the calculations and the results from a test.