A numerical method using the multiple frequencies elliptical whirling orbit model and transient Reynolds-averaged Navier–Stokes (RANS) solution was proposed for prediction of the frequency dependent rotordynamic coefficients of annular gas seals. The excitation signal was the multiple frequencies waveform that acts as the whirling motion of the rotor center. The transient RANS solution combined with mesh deformation method was utilized to solve the leakage flow field in the annular gas seal and obtain the transient response forces on the rotor surface. Frequency dependent rotordynamic coefficients were determined by transforming the dynamic monitoring data of response forces and rotor motions to the frequency domain using the fast fourier transform. The frequency dependent rotordynamic coefficients of three types of annular gas seals, including a labyrinth seal, a fully partitioned pocket damper seal and a hole-pattern seal, were computed using the presented numerical method at thirteen or fourteen frequencies of 20–300 Hz. The obtained rotordynamic coefficients of three types of annular gas seals were all well agreement with the experimental data. The accuracy and availability of the proposed numerical method was demonstrated. The static pressure distributions and leakage flow rate of three types of annular gas seals were also illustrated.