The article presents the results of mathematical modeling of the process of rolling a heat-resistant nickel alloy disk blank. Modeling is carried out by the finite element method using a material model developed on the basis of the results of testing samples for compression and tension at temperatures of 1050, 1100 and 1150 °C and different strain rates. The material model is based on the theory of plastic flow with combined hardening. The developed model makes it possible to take into account the features of material deformation that occur during its cyclic loading at a variable speed, including the change in material parameters during the transition from one speed to another. The model is generalized to the case of non-isothermal loading. A method for identifying the parameters of the model is based on the results of the tests carried out and the obtained material functions are provided. The problem of the rolling process modeling is solved in a three-dimensional setting. To carry out the simulation, the developed model was introduced into the SimuliaAbaqus software package using a user subroutine. Based on the results of the calculation, cartograms of residual stresses, maximum values of plastic deformation, and values of displacements in the axial and radial directions at the end of the rolling process were obtained. The dependence of the change in plastic deformation in the process of rolling in the axial and radial directions is obtained, on the basis of which conclusions are drawn about the features of the deformation of the material in the process of rolling. The reliability of the results of mathematical modeling, the developed deformation model and the method for determining the material functions was confirmed by comparing the disk shape obtained as a result of the calculation with the disk shape obtained during the rolling process.