An initial value problem of a semi-infinite nonlinear viscoelastic bar is solved with continuum damage evolution. The evolution law of the continuum damage for a viscoelastic material is used in order to explore the propagation of two crushing mechanisms: grain boundary cracking and transgranular cracking. Using the method of characteristics, the speed of propagation is found to be dependent on the continuum damage. On the wave front, the delayed elastic strain is zero, and only the continuum damage due to the transgranular cracking evolves. A finite difference method is developed to solve the governing equations on the obtained characteristic lines, and gives a stable solution of the propagation of the stress, strain, and damage. Numerical results are obtained and discussed using the material properties of polycrystalline ice.