Abstract: In relation to the dynamic tests of materials, the approach to solve the viscoelastic wave propagations in split Hopkinson pressure bar (SHPB) tests was summarized. By conducting Laplace transform, the governing partial differential equations were transformed to ordinary differential equations for the image functions, which were solved analytically with suitable boundary equations. Inversely transforming these image functions gives the results of the stress, velocity, and strain in the bar. A wave problem are analyzed to evaluate the internal stress distributions in a viscoelastic specimen occurred in SHPB tests. The problem was solved numerically by way of numerical inverse Laplace transform. A special case when the specimen is pure elastic was solved analytically, giving the exact solution to the problem of elastic wave propagation in a sandwich elastic media.