The formation and structure of normal shock waves in compressible, polytropic gases is investigated using the continuum gas dynamical equations. A phenomenological model for temperature‐dependent viscosity and thermal conductivity is preassumed. The fundamental resulting nonlinear differential equation is solved exactly, and the complete structure of the shock wave is determined. It is found that the flow quantities and characteristics depend upon one parameter, the upstream Prandtl number Pr1, which satisfies the inequality 3&ggr;/(&ggr;+1)≤2Pr1<3, where &ggr; is the ratio of specific heats. For smaller values of Pr1, the strength and compression ratio of the shock increase. Special cases of interest cannot be obtained from this solution and are to be treated independently. Numerical results are given and discussed.