Glimm's method (AD-633 551) is a relatively new numerical technique for solving hyperbolic systems of conservation laws, including those describing compressible fluid mechanics. This report contains an outline of the method, a discussion of the published numerical tests of the method, and some new numerical test results. The latter are one-dimensional models of the effects seen in blast wave propagation. The application of Glimm's method to explosion problems is studied. An appendix is included to indicate how the method can be applied to problems involving a nonideal equation of state. (Author).