Quasi‐isentropic (QI) compression can be achieved by loading a specimen with a low strain rate, long rise time uniaxial strain wave. Recent experimental data show that the quasi‐isentrope of 6061‐T6 aluminum lies a few percent above the principal Hugoniot, that is, at a given specific volume, the QI stress exceeds the principal Hugoniot stress. It has been suggested that this effect is due to material strength. Using Hugoniot data, shock‐reshock, and shock‐unload data for beryllium and 6061‐T6 aluminum, we have constructed the quasi‐isentropes as functions of specific volume. Our results show that the QI stress exceeds the principal Hugoniot stress above a Hugoniot stress of 8.4 GPa in beryllium, and between Hugoniot stresses of 3.8 and 21.4 GPa in aluminum. The effect is due to strength and implies that the QI yield strength can be large. Our calculations show that the QI yield strength is 0.9 GPa in aluminum at a QI stress of 9 GPa, and 5.2 GPa in beryllium at a QI stress of 35 GPa.