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The third-order, nonhomogenized, dynamic method of cells is used to calculate the particle velocity for a shock wave experiment involving an epoxy–graphite laminate. Constitutive relations suitable for the various materials are used. This includes linear and nonlinear elasticity and, when appropriate, viscoelasticity. It is found to be beneficial to incorporate artificial viscosity into the analysis. Artificial viscosity successfully removes the unphysical high-frequency ringing in the numerical solutions of the theory, while leaving the physical oscillations, characteristic of wave propagation in a periodic laminate, largely undiminished. It also allows the viscoelastic relaxed moduli to be closer to their unrelaxed counterparts than in a previous calculation, thus making them more acceptable. The results agree well with the corresponding plate-impact experiment, and are compared to the second-order theory of Clements, Johnson, and Hixson [Phys. Rev. E, 54, 6876 (1996)]. © 1997 American Institute of Physics.