The conservation laws of continuum mechanics and of the kinetic theory with the influence of the angular momentum and associated with its rotation of the elementary volume are considered, the variant of accounting lag is investigated for discrete environment. The analysis of the recording of the Lagrangian function for the collective interaction of the particles with the change of the center of inertia of the moving particles and the effect influence of the angular momentum were used. The equations for gas are calculated from the modified Boltzmann equation and the phenomenological theory. For a rigid body the equations were used of the phenomenological theory, but their interpretation was changed. The nonsymmetric stress tensor was obtained. The Boltzmann equation is written with an additional summand. This situation is typical for discrete environment as the transition from discrete to continuous environment is a key to the issue of mechanics. Summary records of all effects lead to a cumbersome system of equations and therefore require the selection of main effects in a particular situation. The Hilbert paradox was being solved. The simplest problem of the boundary layer continuum (the Falkner-Skan task) and the kinetic theory are discussed. A draw attention at the delay process would be suggested for the description of discrete environment. Results are received for some special cases.