A mechanism of the plastic deformation instability of crystalline alloys is considered in an autowave model of the Portevin-Le Chatelier effect. The model is defined by a system of differential equations for deforming stress, dislocation velocity, the concentration of dissolved impurity atoms interacting with moving dislocations, and forming an "atmosphere" of atoms around them, which provides braking of dislocations. In the model, the distribution of impurity atoms at a certain dislocation rate is considered to be stationary, which is typical for elevated temperatures. In this case, it is shown that the braking force at a dislocation velocity above the critical one has a region of negative sensitivity to the deformation rate, as a result of which the Portevin-Le Chatelier effect is realized. The numerical solution of the original system under the assumptions made showed that the effect manifests itself in the form of relaxation self-oscillations of the deforming stress and the rate of plastic deformation. An expression for the oscillation period is obtained, which is inversely proportional to a given rate of plastic deformation and temperature.