Under the action of relatively low stresses and high temperatures, metallic materials become brittle and fracture with a small value of residual deformations. This problem is known as a problem of thermal brittleness of metals. To solve this problem in the mechanics of materials the damage conception was introduced. To describe the brittle region of the experimental long-term strength curve, the system of simple kinetic equations for the damage parameter and creep deformation was proposed, and the long-term strength criterion was formulated. In this work we proposed to determine the damage parameter changes according to the experimental high-temperature creep curves. Only one kinetic equation for creep rate for compressible medium recorded using the damage parameter in the form of relative density changes is formulated. From this equation the damage parameter is determined depending on the creep rate and the creep deformation. To describe the experimental creep curves various empirical dependences in the form of power, exponential and mixed functions are used. Theoretical damage curves are plotted. The corresponding theoretical long-term strength curves are constructed. Comparison of theoretical creep curves with experimental results for 2.25Cr-1Mo steel at 500°С, 12% Cr-X20 steel at 549.85°С and P91 steel at 600°С is given. A good agreement between the corresponding theoretical and experimental results is observed.