Failure waves in glass were first observed in tests some 50 years ago, with a wave velocity of 1.5-2.5 km/s. In spite of the long time since the discovery of those failure waves, some essential questions concerning them remained unanswered. These are: 1) what is the formation mechanism of those failure waves; 2) what is the propagation mechanism of such failure waves; and 3) what are the kinetics of the failure process? In the past all failure wave researchers assumed that material damage starts from the boundary. But in a recent experimental work on glass [9] they observed that the glass starts to fail within the material behind the shock front, and not from the boundary. This seemingly small change in the way failure waves are formed, makes it possible to predict the mechanics of failure wave formation and propagation, using existing failure models for brittle materials. We’re using here a dynamic failure model for brittle materials that we developed in recent years [10]. To get a failure wave that lags behind the shock front, we assume here that the rate of damage accumulation decreases exponentially with distance from the boundary. This is a plausible assumption, because opening pores and cracks becomes more difficult with distance from the boundary. And indeed, using this assumption we get a failure wave that propagates slower than the shock and at an approximately constant velocity.