In metallic materials under high-temperature creep conditions, the damage evolution occurs. To describe it, Kachanov and Rabotnov proposed the concept of damage. In this paper, the damage parameter is defined as the relative change in material density, serving as an integral measure of damage. By incorporating the damage parameter and the mass conservation law, are we formulated interrelated kinetic equations for rate of creep deformation and the damage parameter. The case of variable loads is crucial both theoretically and practically, as most structural components typically operate under such conditions. Therefore, solutions of considered equations are derived for the case of two-stage loading. The received solutions and experimental results on the creep of titanium alloy under variable loads at 500°C were compared. There is a good agreement between the theoretical results and experimental data.