The linearity of the reflected shock‐velocity‐particle‐velocity (UR‐up) relationship is probed for some materials that already have a linear fit through their initial shock‐wave data. A pure hydrodynamic theory was used in this investigation with no elastic strength of the material taken into account. Based on the result of this analysis, it is concluded that, for all practical purposes, theUR‐up) relationship is linear and can readily be used to calculate the reflected shock Hugoniot. Explicit forms of both first and second coefficients of the relationship are also given.