The process of thermal choking of a subsonic flow of a grey, ideal gas by absorption of thermal radiation from an upstream source is analysed. The flow may be considered produced by a shock. Calculations for streamwise variation of flow properties are presented, and, for the radiation‐dominant case, an initial transparent process, a final Rosseland process and a matching solution are found analytically. A simple model is given for finding the radiation source temperature required to produce choking.