The mechanism of localization of low-temperature plastic deformation is investigated within the framework of the thermal activation model. The localization mechanism is considered as a result of the autowave character of the stationary solution of a system of equations that describes both the processes of thermal conductivity and plastic deformation. It is established that the stationary solution of the initial problem is given by the wave fronts of switching waves of temperature and plastic deformation. It is shown that the considered autowave mechanism determines the process of localization of high-temperature areas of plastic deformation in the cross-section of the sample in the form of either a neck or separate deformation bands.