The phenomenon of cyclic creep acceleration (CCA) is well known. Also, it has been observed experimentally that there exists a peak stress level above which CCA begins to occur. For copper the value of this peak stress is known to be independent of cyclic stress conditions such as stress amplitude and frequency. This stress level or the threshold stress was observed to increase with temperature in the range 0.4 to 0.5T m. A model is suggested to predict the threshold stress level and to explain the temperature dependence of the stress. This model is based on the dislocation core diffusion process by the athermally generated excess vacancies. The concept of critical length of dislocation core is used for core diffusion fast enough to enhance dislocation climb. This critical length is expressed as a function of stress and temperature. From these concepts, the threshold stress is expressed asτ/G - A exp (-ΔQ/RT). The experimentally observed values of the threshold stress are in good agreement with this model, and the temperature dependence is also experimentally proved.