Stability of resistive balloon modes of a finite-pressure plasma in traps with spatial magnetic axis and corrugated magnetic field is investigated. Stability criteria of the modes indicated are obtained in the near-the-threshold region and unstable oscillation increments are determined. It is shown that a slow resistive mode is stabilized with the growth of plasma pressure, while the fast resistive mode remains unstable under arbitrary plasma pressure values. Results of stability criterion numeric analysis show that a destabilizing effect of magnetic field corrugation leads to the resistive balloon mode stability zone narrowing by plasma pressure by about 10%. 12 refs.; 2 figs.