The deviator constitutive relation of the proposed theory of plasticity has a three-term form (the stress, stress rate, and strain rate vectors formed from the deviators are collinear) and, in the specialized (applied) version, in addition to the simple loading function, contains four dimensionless constants of the material determined from experiments along a two-link strain trajectory with an orthogonal break. The proposed simple mechanism is used to calculate the constants of themodel for four metallic materials that significantly differ in the composition and in the mechanical properties; the obtained constants do not deviate much from their average values (over the four materials). The latter are taken as universal constants in the engineering version of the model, which thus requires only one basic experiment, i. e., a simple loading test. If the material exhibits the strengthening property in cyclic circular deformation, then the model contains an additional constant determined from the experiment along a strain trajectory of this type. (In the engineering version of the model, the cyclic strengthening effect is not taken into account, which imposes a certain upper bound on the difference between the length of the strain trajectory arc and the module of the strain vector.)