By means of the two-scale expansion method, it is found that the propagation of the plane, cylindrical and spherical waves in the thermally unstable medium is accompanied by their breaking and shock wave formation. It is shown how the simple wave solution can be generalized for the case of the shocks. It is established that, in contrast to the case of the adiabatic motion, the amplitude growth rate and the distance of the wave breaking can both increase and decrease in the inhomogeneous gas for the waves of the fixed propagation direction (in comparison with their values for the gas with the constant initial density). The stationary waves of finite amplitude can exist in the presence of the dissipative effects under certain initial conditions. The obtained results confirm the conclusion about the unstable travelling waves as the source of the inhomogeneities and shock waves in the \(H_ 2\) clouds and in the neighbourhood of compact H II regions.