Mass escape rate of mon- and diatomic gases from a planetary atmosphere is studied based on Parker's model for a broad range of surface conditions. The escape rate is found to follow two asymptotic regimes, namely, high-and low-density regimes, with a short intermediate regime between them. Equations for the escape rate in every asymptotic regime are found theoretically. A comparison of the obtained escape rates with results of recent kinetic simulations shows that Parker's model satisfactorily predicts escape rates only in the high-density regime. Based on this finding, a criterion of applicability of Parker's model for the calculation of the mass escape rate is established.