Longitudinal stress profiles have been measured in polycrystalline silicon carbide (SiC) shocked to peak stresses from 7.3 to 23 GPa. Dispersive wave fronts, consistent with the expected inelastic response, were observed beyond the previously reported Hugoniot elastic limit (HEL) of 11.7 GPa. Detailed numerical analyses were carried out to interpret the observed inelastic response using both a strain‐hardening, plasticity model and a pressure‐dependent strength, stress relaxation model. Both models show good agreement with the data; the latter provides a better fit to the transient features in the measurements suggesting rate dependence in the material response. The computed Hugoniot curve matches all of the peak state data for two different types of SiC that display more than 20 % variation in HEL. This suggests that the measured HEL for SiC is not a proper indicator of the material strength in the shocked state. The results also show that the longitudinal data and analyses are insufficient to resolve issues related to material strength and mechanisms governing inelastic deformation in shocked SiC. The need for a more complete characterization of the shock response of a high‐strength brittle material is discussed. ©1996 American Institute of Physics.