A continuum damage model developed to describe the rate-dependent dynamic response of laminated polymer composites is investigated for its behavior during strain-softening. The formulation is shown to lead to mathematically well-posed wave propagation problems as well as to unique and stable solutions. Numerical simulations of unidimensional wave-propagation in the through-thickness direction of a transversely isotropic laminate are performed. For a realistic range of damage propagation time constants the results are shown to be mesh insensitive and convergence to a finite amount of dissipated energy is obtained; two issues of concern in modeling dynamically strain-softening solids. Thus the model is validated with respect to strain-softening regimes.