The need for high turbopumps efficiency makes labyrinth seals a wide diffused subsystem in space engines. The role of this non-contacting shaft seal is to reduce flow leakage and to limit recirculation through rotor/stator gaps in pumps and turbines. The high fluctuations of pressure and velocity deriving from their operation, together with the necessity for light structures, lead labyrinth seals to be subject to aeroelastic instabilities, object of in-depth investigations in order to prevent failures caused by fatigue and provide safer turbopumps. This work presents the stability analysis of a straight-through two-fins labyrinth gas seal resulting from the variation of working conditions and parameters, in order to investigate how the latters can affect the system behavior in the case of an isentropic flow and strong fluid-structure coupling.