Labyrinth seals are widely used in rotating machinery and can be prone to aeroelastic instabilities. The rapid development of computational fluid dynamics now provides a high-fidelity approach for predicting the aeroelastic behavior of labyrinth seals in three dimension and exhibits great potential within industrial application, especially during the detailed design stages. In the current publication a time-marching unsteady Reynolds-averaged Navier-Stokes solver was employed to study the various historically identified parameters that have essential influence on the stability of labyrinth seals. The findings from the numerical approach agree well with analytical criteria in determining the overall stability of the seal structure while being able to capture the acoustic behavior of the upstream or downstream large cavities and its influence on the inter-fin cavities. The high-fidelity approach provides additional insights on the effects of nodal diameter, travelling wave direction, pressure ratio, and the linearity of the phenomenon for relatively large vibration amplitudes, all of which can aid during the design space exploration.