Present study simulates oscillatory supersonic impinging jet flows using the axisymmetric Navier-Stokes code. To capture the salient features of flow oscillation and overcome the divergence during the initial transient period, several tests have been conducted for the grid and time step sizes. The results also show that the effects of the inlet flow condition at the nozzle exit and turbulence on the oscillatory behavior of supersonic impinging jets are negligible. Frequencies of the surface pressure oscillation obtained by the selected numerical method are in good accord with the measured impinging tones for various cases of nozzle-to-plate distance. Two seemingly different staging behaviors with nozzle-to-plate distance and nozzle pressure variations are found to correlate well if the frequency and distance are normalized by the length of the first shock cell.