A stress-strain state and a time duration up to fracture are calculated with allowance for two-stage behavior of a rotating disk under creep conditions. The duration of the stages is investigated depending on the choice of the version of the creep kinetic theory and the geometric dimensions of the disk. The first stage is the accumulation of damage and the beginning of fracture in some area of the body, where the accumulated damage reaches a critical value. The second stage is the spread of the fracture front and the complete destruction of the body. A calculation method has been developed which reduces the solution of the unsteady-state creep problem to the solution of an analogous steady-state problem.