A design of the tunable superconducting power filter is described. The filter consists of superconducting microwave cavities with a mechanical tuning method. The electromagnetic simulations using niobium cavity suggested that there were conditions where the resonator with high-unloaded Q can realize a fractional center frequency change of more than ± 10% by using a Nb rod moving in the cavity. The simulations approximated the resonant frequency dependence of the rod moved by a cryogenic actuator in the tunable cavity experiment. In addition, the simulation of the power handling capability showed a feasibility of the value more than 50dBW.