The stability of the vertical position control system in TCV is analysed using two different plasma models, a deformable plasma model (DPM) and a rigid plasma model (RPM). The open loop growth rates and closed loop stability are computed, as functions of various plasma parameters, for both models. It is found that the difference between the open loop growth rates predicted by the two models depends significantly on plasma elongation and triangularity. Growth rates are also computed using the NOVA-W code, and good agreement is found with the DPM results. The stability of the closed loop system is analysed as a function of the feedback gain settings. The size of the stable domain in gain space is evaluated for the DPM and RPM models as a function of plasma elongation and triangularity, and the effect of varying the vertical position observer is shown. The stable domains, as predicted by the two models, are consistent with the experimental observations obtained from a highly elongated, D shaped plasma in TCV (n = 2.55).