The processes of complex plastic deformation of polycrystalline structural alloys along flat trajectories of arbitrary curvature are considered. The version of the equations of state of thermoplasticity used in this article is based on the concept of a yield surface and the principle of gradient of the plastic strain rate vector to the yield surface at the loading point. This version of the equations of state reflects the main effects of elastoplastic deformation of the material for arbitrary complex deformation trajectories. Particular attention is paid to the issues of modeling the processes of elastoplastic deformation of polycrystalline structural alloys for complex deformation processes accompanied by rotation of the main areas of stress tensors, total and plastic deformations. Material parameters and scalar functions included in the constitutive relations of the mathematical model of thermoplasticity for steel 45 used in this work were obtained. To assess the degree of reliability and determine the limits of applicability of the constitutive relations of thermoplasticity, numerical studies of complex plastic deformation of steel 45 with a yield plateau along flat trajectories of arbitrary curvature were carried out: flat piecewise broken trajectory of the “hourglass” type; two flat trajectories, symmetrical with respect to the bisector of a right angle, representing a quarter of a circle and a straight section with a trajectory bend of 90°. It is shown that the thermoplasticity model used in the work qualitatively and with the accuracy necessary for practical calculations quantitatively describes the main effects of complex plastic deformation of steel 45 with a yield plateau under loading along flat trajectories of arbitrary curvature.