This is the second of a two-part study on the propagation of stress gradient in composite materials. In this paper the propagation of stress gradient behind the wave front in an elastic medium is investigated. It is shown that the stress gradient does not maintain the same sign as the wave front is propagated. The implication of this result is that the plastic yield can occur at places behind the wave front before it occurs at the wave front even if the initial wave has a discontinuous rise in stress at the wave front followed by a gradual decrease in magnitude behind the wave front. Numerical examples are presented for plane and circular pressure waves propagated through an inclusion of various shapes.