This research deals with the vibration of rotors containing liquid, such as rotors of washing machines with a fluid balancer, and is intended to predict the occurrence of self-excited vibration and to evaluate some other characteristics of these rotors by analysis. We developed an analytical method using the assumption of shallow-water sloshing to predict the motion of liquid contained in a whirling ring, and made some calculations for various whirling rates. These calculations confirmed the validity of the method, and yielded following results. (a)Not only major resonances, but also secondary resonances peculiar to nonlinear systems occur when multiples of the exciting frequency correspond to natural frequencies of sloshing. (b)There are some isolated waves(or solitons)near resonance points, and the number of solitons changes when whirling rates changes slightly.