There exist a number of observations of magnetohydrodynamic (MHD) activity that can be related to resistive MHD modes localized near the plasma boundary. To study the stability of these modes, a free boundary description of the plasma is essential. The resistive plasma–vacuum boundary conditions have been implemented in the fully toroidal resistive spectral codecastor(Complex Alfve´n Spectrum in Toroidal Geometry) [Proceedingsofthe18thConferenceonControlledFusionandPlasmaPhysics, Berlin, edited by P. Bachmann and D. C. Robinson (European Physical Society, Petit‐Lancy, Switzerland, 1991), p. 89]. The influence of a free boundary, as compared to a fixed boundary on the stability of low‐mtearing modes, is studied. It is found that the stabilizing (toroidal) effect of a finite pressure due the plasma compression is lost in the free boundary case for modes localized near the boundary. Since the stabilization due to the favorable average curvature in combination with a pressure gradient near the boundary is small, the influence of the pressure on the stability is much less important for free boundary modes than for fixed boundary modes.