The aim of this paper is to discuss the modified Navier-Stokes equations and to find the reason for appearing the second viscosity and cross flow through the sides of elementary volume at large gradients of the physical values. The modified laws of conservation were obtained for the particles without structure in gas, liquid, and solid taking into account the influence of angular momentum. The equilibrium conditions formulated as the conditions of angular momentum equilibrium for continuous mechanics with boundary conditions were suggested in previous works. The equilibrium conditions for forces are a special case of more general conditions of angular momentum equilibrium and follow from them. We discuss also the problems that can appear if the variation of angular momentum in an elementary volume near a surface takes place.