The relativistic Rankine‐Hugoniot shock wave conditions of Taub are extended to include radiation pressure and energy density. Specialization to the situation of a nonrelativistic ambient gas gives strong shocks, and solutions are obtained separately for the cases of a pure material gas and a pure radiation gas behind the shock. The material gas is considered to have a constant adiabatic exponent &ggr; ≤ 2, or to be itself relativistic, and the value&ggr;=43gives the radiation gas results. The rest density compression increases above its nonrelativistic strong shock limit (&ggr; + 1)/(&ggr; − 1), by a term proportional to &bgr;2in the lowest order, where &bgr; is the ratio of shock velocity to light velocity. As &bgr; → 1 (extreme relativistic strong shock) the rest density compression goes as 1/(1 − &bgr;2)½, but there is no setting‐in of degeneracy in the shocked gas. In shock coordinates, the flow velocity ratio across the shock (front to back) decreases monotonically from its nonrelativistic limit and approaches the value 1/(&ggr; − 1) as &bgr; → 1. An expression is also obtained for the velocity of relativistic sound wave propagation in a mixture of a thermally perfect material gas and a radiation gas.