The discontinuous forms of the full Navier‐Stokes equations are derived. A general method of solving linearized initial and boundary value problems is discussed. The following specific examples are solved: initial value problem in an unbounded domain, shock reflection from an insulating wall, shock evolution in a finite shock tube with insulating walls, and reflection of a sound wave from an isothermal wall. In all cases the dissipative parameters and the gas law are left arbitrary.