The state of the crystalline medium under the conditions of thermal fluctuations and mechanical stresses called weakly stable is determined by the displacement of atoms at a relative distance of 0.15-0.20 from the equilibrium positions. Such a displacement of the atoms follows the Lindemann criteria of the crystals melting, and the state of atomic ensemble can be described as delocalized one. The state of delocalization means the transition of the atom through the maximum of interaction force and is characterized by a strong anharmonic component of oscillations and softening of elastic modules. It is the state of delocalization of the atomic ensemble that is the weakly stable state of the crystal lattice. Weakly stable state of metal materials is manifested in a wide range of phenomena. These include abnormal reduction of elastic modules in thermoelastic martensitic transformations, second-order structural-phase transitions with the formation of long-period structures, abrupt plastic deformation, most clearly manifested in aluminium and its alloys, increasing the rate of deformation during creep in the ultrasonic field under static load. This paper presents the results of the analysis of the weakly stable state of the crystalline medium, especially in plastic deformation, that is, in the processes caused by the displacement of atoms from the equilibrium position. In these processes, the weakly stable state of the system can occur in the field of mechanical stresses and thermal fluctuations when the acoustic field of standing waves is applied, formed by primary acoustic emission signals, the combined action of which allows to overcome the potential barrier. In this state, the oscillatory displacement of the acoustic standing wave acts as a factor of self-organization, that is, it may be sufficient to activate the correlated dislocation slip, in fact, the athermal above-barrier slip in the weakly stable state of the crystal lattice.