For developing laser propulsion, it is very important to analyze the mechanism of Laser‐Supported Detonation (LSD), because it can generate high pressure and high temperature to be used by laser propulsion can be categorized as one type of hypersonic reacting flows, where exothermicity is supplied not by chemical reaction but by radiation absorption. I have numerically simulated the 1‐D and Quasi‐1‐D LSD waves propagating through an inert gas, which absorbs CO2gasdynamic laser, using a 2‐temperature model. Calculated results show the fundamental properties of the non‐equilibrium LSD Waves. © 2004 American Institute of Physics