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It has been traditional to use the fluid approximation when using solid Hugoniot data to construct a constitutive equation for the pressure as a function of volume and energy. The tradition rests on the assumption that material strength is negligible at large pressures, and the unavailability of Hugoniot shear stress data. However, material strength may be non‐negligible, even at large Hugoniot stresses, and a method for calculating shear stresses along the Hugoniot has been developed, so that in principle, P(V,E) can be constructed without making the fluid approximation. Using beryllium as an example, we show how to construct P(V,E), taking material strength into account. We also show that the calculated shear stresses along the Hugoniot are less than the actual values, due to assumptions that are made to reduce the data. Thus, the resulting ratios of the Hugoniot shear stress to the Hugoniot pressure underestimate the actual values. In beryllium, this ratio varies from 0.07 at 5 GPa to 0.015 at 35 GPa.