This article deals with two-frequency oscillations of the shallow cylindrical shell on which acts small, superficial, disturbing force directly to middle shell surface. This force is with two frequencies of the undisturbing shell oscillation. By means of asymptotic methode Krilov-Bogoljubov-Mitropolski's the differential equations of the first approximation are derived and they enable the analysis of amplitudes and phasis behaviour during stationary and nonsta-tionary oscillation mode. Since the frequencies of the forced power are close to two own frequencies, the resonance modes that are the most interesting for the point of the processes that are arising are exemiend.