The fracture behavior due to dynamic response in a composite cylinder subjected to a moving pressure has been investigated. The resonance of stress waves can result in very high amplitude and frequency strains in the cylinder at the instant and location of pressure front passage, when the velocity of the moving pressure approaches a critical velocity. The stress wave with high magnitude, while short in duration, might not cause structural failure immediately. However, it could accelerate the propagation in the cylinder with initial imperfection and shorten fatigue life of the cylinders. The fracture mechanism induced by dynamic amplification effects is especially critical for overwrapped composite cylinders because of the multi-material and anisotropic construction, thermal degradation in material properties, and a design goal inherent in lightweight structural applications.