The paper is focused on creep-rupture tests of samples made of the 2024 alloy in the T3511 temper under uniaxial tensile stress conditions. The basic characteristics of the material at the temperatures of 100, 200 and 300 °C were determined, such as the Young’s modulus E, yield point σy, ultimate tensile strength σc and parameters K and n of the Ramberg–Osgood equation. Creep tests were performed for several different levels of nominal axial stress (load) at each temperature. It was observed that in the process of creep to failure at 200 and 300 °C, as the stress decreases, the creep time increases and, at the same time, the strain at rupture increases. However, such a regularity is maintained until a certain transition stress value σt is reached. Reducing the stress below this value results in a decreased value of the strain at rupture. A simple model of creep damage accumulation was proposed for the stress range above the transient value. In this model, the increase in the isotropic damage state variable was made dependent on the value of axial stress and the increase in plastic axial strain. Using the results of experimental creep-rupture tests and the failure condition, the parameters of the proposed model were determined. The surface of fractures obtained in the creep tests with the use of SEM technology was also analyzed.