The rheological behavior of a brittle, strain‐rate sensitive, polycrystalline, organic solid explosive (pressed TNT) was investigated under conditions of uniaxial compressive strain. The wave structure of shocks introduced into the specimen material was determined by examining quartz stress transducer records. An ``elastic precursor'' wave forms in the specimen if the driving stress is below approximately 10 kbar. The length, shape, magnitude, risetime, and velocity of the precursor wave and the risetime of the follower wave are functions of both the specimen thickness and driving stress. Stress‐strain‐variable‐strain‐rate curves and corresponding Hugoniot curves were experimentally determined for two specimen thicknesses. All sets of curves were found to be related to specimen thickness. Shock hydrostats were estimated at the lower strain levels from those stress‐strain‐constant‐strain‐rate curves most closely in agreement with the Hugoniots. A simple elastic‐plastic theory that incorporated the results from an associated uniaxial stress study was used to determine the deviatoric stress component. The isentropic and isothermal hydrostats were deduced from the shock hydrostats; the isothermal curves were compared with experimentally obtained results. A numerical study indicated that transducer data were not significantly affected by wave reflections and interactions. Also verified was the adequacy of the simple elastic‐plastic model used to describe the loading response.