Abstract Labyrinth seals are a widely used non-contacting mechanical subsystem of space engines turbopumps. Thanks to a sequence of teeth and cavities, they provide to the working flow a tortuous path limiting leakage and recirculation phenomena through rotor/stator gap and they guarantee more efficient engine performances. The high fluctuations of pressure and velocity experienced by the flow running through labyrinth seals, together with the necessity for light structures, make them subject to aeroelastic instabilities. This problem is object of in-depth investigations in order to prevent failures caused by fatigue and provide safer turbopumps. In this work, the analysis of a straight-through one-cavity labyrinth gas seal stability is conducted through the development of a Navier-Stokes one-dimensional fluid model monolithically coupled to an elastic structure model. To this end, a sensitivity study to the variation of different parameters is presented, with a particular focus on the role of the energy equation, the leakage flow formulation and, for a viscous flow, the shear stress model. This study allows to characterize the role that different assumptions and working parameters have on the stable/unstable behaviour of a labyrinth gas seal, under the hypothesis of a strong fluid-structure coupling. The achieved results show how the characteristic of the fluid modelling can be crucial for the accurate representation of the aeroelastic problem and how the choice of the leakage flow and friction coefficient model, together with the sizing of some geometric parameters, can have a decisive impact on the system stability.