The conditions for generating rotary sloshing of liquid, and the influence of operational conditions, such as the size of equipment, liquid height and rotational speed of impeller in a stirred vessel with a flat paddle impeller on the rotary sloshing frequency and resonance phenomena were examined. It was found that the rotary sloshing of liquid occurred immediately after the liquid surface touched the lower end of the impeller, and that it was generated when the rotational speed of impeller was greater than the rotary sloshing frequency. Moreover, based on the equation for sloshing frequency in the tank without an impeller, the equation of rotary sloshing frequency was derived considering the influence of the impeller's diameter. Furthermore, in the mixing machine, when rotary sloshing of liquid occurred, the vibration was induced by both rotational speed of impeller and rotary sloshing. It was found that the resonance phenomena occurred when the vibration induced by rotary sloshing of liquid was in agreement with the natural frequency of the mixing machine.