Internal resonance in the vibration of a floating roof coupled with nonlinear sloshing in a circular cylindrical oil storage tank is investigated. The nonlinear system exhibits internal resonance when nonlinear terms of the governing equation have a dominant frequency close to a certain modal frequency of the system. Numerical results show that when internal resonance occurs, the responses of stresses in a floating roof exhibit a long-duration period of large amplitude despite a short duration of the earthquake excitation applied to the tank. Due to the presence of internal resonance, the underestimation of the stresses associated with the use of the linear theory becomes more marked, and thus the importance of nonlinearity of sloshing in the stress estimation is accentuated. It is illustrated that the magnitudes of the stresses increase with the increase in the liquid-filling level, and that the effect of internal resonance on the stresses noted in the case of sinusoidal excitation appears under real earthquake excitation. A method for reducing the stresses is proposed.