Jet-induced rotary sloshing caused by an upward periodic jet in a partially filled cylindrical container is computationally simulated for investigating a stable sloshing condition and its basic characteristics under various values of AQ, Tjet and QL0 in a given function of the inlet jet: QL(t) = AQ sin[(2π /Tjet)t] + QL0. Then, the stable rotary sloshing is found not to be observed when either the minimum or maximum flow rate of QL(t) reaches a threshold value of the sloshing-occurrence boundary. The free surface motion like a beat phenomenon caused by interference between the sloshing wave and the periodicity of the inlet jet is also observed in the signal of the free surface elevation. Furthermore, the period of the envelope seems to match with Tjet, and this phenomenon is successfully formulated by the superposition between the sloshing wave and the free surface wave due to the periodic inlet jet.