Thermo creep deformations for most heat-resistant alloys, as a rule, nonlinearly depend on stresses and are practically non- reversible. Therefore, to calculate the properties of these materials the theory of plastic flow is most widely used. Finite-element computations of a stress-strain state of structures with account of thermo creep deformations up to now are performed using main commercial software, including ANSYS package. However, in most cases to solve nonlinear creep equations, one should apply explicit or implicit methods based on the Euler method of approximation of time-derivatives. The Euler method is sufficiently efficient in terms of random access memory in computations, however this method is cumbersome in computation time and does not always provide a required accuracy for creep deformation computations.

The paper offers a finite-element algorithm to solve a three-dimensional problem of thermo creep based on the Runge-Kutta finite-difference schemes of different orders with respect to time. It shows a numerical test example to solve the problem on the thermo creep of a beam under tensile loading. The computed results demonstrate that using the Runge-Kutta method with increasing accuracy order allows us to obtain a more accurate solution (with increasing accuracy order by 1 a relative error decreases, approximately, by an order too). The developed algorithm proves to be efficient enough and can be recommended for solving the more complicated problems of thermo creep of structures.