The fatigue loading of the [0_n/90_m/0_n]-laminates is accompanied by the formation of multiple matrix cracks, crossing the inner 90 -layers. This process is sufficiently non-uniform both in space and in time (number of cycles being the measure). The description of all damage mechanisms in terms of unified model seems an overcomplicated task, thus the main attention in this work is being paid to the damage accumulation, generation of transverse cracks and their interaction with damage and to the effect of stochasticity on these processes. The elaboration of a model of the stochastic fracture of composites is preceded by the analysis of the various features of the damage accumulation under more simple model conditions. (orig./RHM)SIGLEAvaila...