Fundamental experiments are carried out to examine the parameter that dominates slip band initiation in copper electroplating under the condition where the mean stress as well as the stress amplitude varies. It is found that, in the case of constant amplitudes stressing, the relation between the proper stress σp for slip band initiation and the number of cycles N is well represented by σαp·N=C. This mean that slip bands appear when the total hysterisis energy applied to the copper plating attains a critical value. when the mean stress varies stepwise or sinusoidally, the range pair of the stress mainly dominates the occurrence of slip bands, and Miner's rule holds for the accumulation of fatigue damage. Accordingly, the parameter (√σαi)1/α, where σi is the range pair and α is the exponent of the σp-N relation, is equivalent to the proper stress under constant amplitude stressing. Based on these results, the applicability of the copper plating to the fatigue gage that accumulates and indicates a load experience is discussed.