A nonlinear model of the process of low-temperature discontinuous yielding of metals has been constructed, which allows the totality of strain jumps to be described as a function of the mechanical properties of material and dynamic characteristics of the loading system. The adequacy of the model has been experimentally verified for austenitic steel and an aluminum alloy.Introduction. Deep freezing (T < 30 K) gives rise to an effect of low-temperature jumplike deformation [1]. It is accompanied by considerable heating and localization. A load decrease, which reaches more than a half of the initial level for some materials, corresponds to each jump. Such an abrupt change from elastic deformation to adiabatic plastic flow is typical of high-strength steels and alloys and is a jumplike decrease in the load-carrying ability of structural element with possible reaching of excessive strain or fracture. The manifestation of the effect depends in a complex manner on the properties of material and loading conditions. The modeling of the jumplike deformation process makes it possible to greatly reduce complex and expensive multiple-factor experimental investigations in liquid helium.Among the works that are currently under way in this direction, [2][3][4][5][6][7][8][9] are noteworthy. The model presented in [2] is based on informatics methods (cellular automatons), and the models considered in [3, 4] may be conventionally classed as "physical" ones, for they include not only characteristics of dissipation and heat-exchange processes with reference to the thermal mechanism of adiabatic deformation, but also dislocation parameters and give therefore only qualitative description of the phenomenon. In [4], a model constructed on the basis of the so-called electromechanical analogy was also proposed. The purely mechanical model [5] allows one to study the effect of the magnitude of overload as an analog of thermal softening and other factors on the development of strain jump at room temperature. In [6], the jump process in the case of twinning of aluminum alloy single crystals is modeled mathematically with assumptions of the instantaneous application of driving force and the absence of strain hardening. However, the possibility of nonisothermality of the process and other peculiarities of deformation of metals at temperatures close to absolute zero are not considered. Such peculiarities and the influence of effective mass are not taken into account either in the formulation of the model presented in [7], driving force being absent. The model presented in [8], which was constructed for the estimation of jump duration, proved inadequate in respect to this characteristic since it does not include inertial force, and load is applied instantly. The model presented in [9], which was developed in order to obtain an analytical solution for its investigation, describes not precisely enough in some cases the jump process since it does not take into account such peculiarities of deformation as hardening variation and its nonlinear nature...