The failure wave phenomena in glass media under shock loading are analyzed. The propagating mechanism and dynamic characteristics of failure wave and the property of failure layer are revealed. On the basis of experimental analysis, a damage accumulating model determinated by partial stress impulse is proposed, which describes the phenomenon of failure delay in materials being done with the Heaviside function. The propagating procedure, the evolution characters of transverse stress and longitudinal compression strain in failure layer are simulated. Furthermore a phenomenon is revealed that the failure wave velocity decreases after reflection of rarefaction wave at the boundary of failure layer.