Sinusoidal vibration has practical value as a substitute for random vibration in equipment qualification testing. How and when to employ a sinusoidal substitution is discussed in this paper. In particular, a damage criterion is discussed, which relates the number of sinusoidal peaks occurring while passing through a resonance to the number of random peaks exceeding a specified amplitude value.Formulas are given for the sine‐random response relationship, with formulas and a diagram for the random test duration to be used with the amplitude relationship.