Squeal noise of rail-bound vehicles emitted in tight curves is characterized by high sound pressure levels at pure medium and high frequencies. The models used to simulate the vibrations that cause this noise differ in particular in terms of the instability mechanisms considered: negative damping introduced into the system due to the decrease in the friction coefficient with the sliding speed or instability with a constant friction coefficient. The objective of the paper is to contribute to the understanding of the instability mechanisms in the case of a constant friction coefficient. A stability analysis of the wheel/rail contact in curve is performed by using an equivalent point contact model (Hertz?s theory for normal contact and assumption of full sliding equilibrium states for tangential contact). The wheel/rail responses are computed by using wheel and rail modal bases. Results show that even with an assumption of a constant Coulomb friction coefficient, instabilities can indeed occur due to the coupling between normal and tangential dynamics in the wheel/rail system. This coupling can involve two wheel modes or only one when rail dynamics is included. The vertical dynamics of the rail then play an important role in the occurrence of the instability.