The hydrodynamic stability of a steady, plane, step shock through a fluid medium with arbitrary equation of state is investigated through consideration of the initial‐value problem for the time‐dependent hydrodynamic equations, linearized in perturbations from the steady flow. If the stability function,Fs= 1 + &kgr; ‐ &kgr;2(v1‐v)pS/T(with &kgr; the Mach number,vthe specific volume,Tthe absolute temperature,pSthe entropy derivative of pressure at constant volume, and subscript 1 referring to the preshock state) is negative, disturbances grow exponentially with time and the shock is unstable. The character of the shock Hugoniot with respect to stability is discussed.