In arbitrary curvilinear coordinate system under elastoplastic deformation, a comparative analysis of three

variants of the constitutive equations at the loading step was performed. In the first variant, the equations of

the theory of plastic flow were used, according to which the strain increment had been divided into elastic

and plastic parts. The cumbersomeness of the algorithm for obtaining expressions for the components of the

plastic strain increments tensor in an arbitrary curvilinear coordinate system is shown, which leads to the lack

of the possibility of obtaining the matrix dependence of physical equations at the loading step. In the second

variant, to obtain plastic strain increments, the hypothesis of their proportional dependence on the

components of the stress increments deviator was used. The constitutive equations were also obtained by

summation of the elastic strains increment and plastic strains increment. In the third variant, the hypothesis

of the division of strain increments into elastic and plastic parts was not used. The physical equations were

written using the assumption that there was a proportional dependence between the components of the strain

increment deviators and stress increment deviators. Using the example of calculating the shell of revolution,

the preference of the third variant of the constitutive equations for elastoplastic deformation is shown.