The method to predict time to failure of roof covering rubber sheets under fluctuating ozone concentration and temperature was developed, being based on the equation, t=10^<(c/t+D)>/X^A, which express the time to failure of them, at constant ozone concentration, X and temperature, T. Ozone tests which ozone concentration and temperature were varied through sine curves were carried out. Comparing both results obtained by the tests and calculation, it is concluded that the effect of fluctuating ozone concentration and temperature can be estimated by the integration of them with time.