Primary containment computer codes, REXCOHEP (Lagrangian), ICECO (Eulerian), ALICE (ALE), and REXALE (ALE), developed in the Engineering Mechanics Program of Argonne National Laboratory, were validated by performing comparison with the analytical solution and experimental data. Three problems were used. The first problem deals with the propagation of shock wave in a rigid tube for which analytical solution exists. The second problem concerns the response of a simple flexible vessel to a hypothetical core disruptive accident (HCDA)-in-duced pressure loading for which experimental data exist. The experiment was performed with a well-defined and calibrated energy source. It provided reliable test data for code validation. The third problem concerns the propagation of shock wave in a three-dimensional space for which the experimental data exist. Results of the comparisons show that the Lagrangian, Eulerian, and ALE codes can all give acceptable solutions to the shock wave propagations and on the response of containment vessel to HCDA-induced pressure loading.