Comparative analysis of the use of the defining equations of plasticity theories obtained at the loading step in three ways is performed. In the first method, the relations between strains increments and stresses increments are obtained by differentiating the governing equations of the small elastic-plastic deformations theory between full stresses and strains. In the second method, the authors based on the proportionality hypothesis between the component deviators of strains increments and the component deviators of stresses increments without separating the incremental strain into elastic and plastic parts obtain the determining equations at the loading step. In the third method, the relations between the incremental strain and the stresses increment of the plastic flow theory are used on the basis of the hypothesis about the proportionality of the plastic deformations increments to the components of the stress deviator. Based on the analysis of algorithms for obtaining the constitutive relations and the analysis of the numerical results of the calculation example, preference is given to the second method of obtaining expressions between stress increments and strain increments without separating the latter into elastic and plastic parts.