Kinetic theory approach is proposed for the plane thermomechanical problem. Tamm’s variational method, developed to describe shock wave propagation in the infinite medium, is extended to unsteady problems with the boundaries. A novel feature of the proposed procedure is the use of the stochastic form of the Boltzmann equation with the trial function constructed from the two local half‐Maxwellian distribution functions. In the collision integral, micro and macro variables are separated with the help of the auxiliary coordinate systems to facilitate integrations.