Kinetics of mass transfer in thin metal films during electromigration was analyzed as a function of the generated internal stress. Stress evolution was considered for the case when two different stress relaxation mechanisms can operate simultaneously near the anode end of the strip: thresholdless diffusional creep through a fixed aperture, and diffusional creep with a threshold stress, σt, through the same aperture. Stress distribution and electromigration rate were found as explicit functions of the film length, the aperture size, and the current density. The apparent threshold length was analyzed. It was shown that an apparent threshold product can grow with the current density, in agreement with the experimental results.