The theory of stability and saturation of nonlinear ballooning modes in tokamaks is developed using a generalised Archimedes’ principle which is justified for thin elliptical flux tubes. The equation of motion in general geometry is derived and then applied to a simplified ‘s-a’ equilibrium and the nonlinear dynamics of this equilibrium are investigated. This theory shows that the whole pressure and magnetic shear profile is important for nonlinear stability, rather than just the local values which are used for linear stability. The theory shows that for a given pressure profile, nonlinear ballooning saturated states are possible even if the profile is linearly stable to ballooning modes at all radii; the nonlinear ballooning modes are metastable. This occurs particularly at low magnetic shear. The amplitude of the displacement can be as large as the pressure gradient scale length. We conjecture that triggering a transition into these filamentary states can lead to hard instability limits. A short survey of different pressure profiles is presented to illustrate the behaviour of the system.