The thickness dependence of the electrical stability under monotonic and cyclic tensile loading is investigated for Cu films on polymer substrates. As for monotonic tensile deformation, thicker films show better stability than thinner films due to their higher ductility and the larger capability of strain accommodation. For the fatigue resistance, however, a more complex behavior was observed depending on the amount of the applied strain. For low strain amplitude in the high cycle fatigue (HCF) regime, thinner films exhibit longer fatigue life because the larger strength of thinner films suppresses dislocation movement and damage nucleation. However, for high strain amplitudes in the low cycle fatigue (LCF) regime, the fatigue life for thinner films is drastically reduced compared to thicker films. It is shown that fatigue coefficients in the LCF regime can be obtained when applying the Coffin–Manson relationship.