The results of a study on the non-linear stability of tearing modes for hollow current profiles in cylindrical geometry are presented. Their non-linear evolution which, through magnetic island formation, leads either to saturation of the tearing mode (a new non-axisymmetric equilibrium is reached) or to a re-distribution of the flux and field line reconnection in Kadomtsev's sense (a new axisymmetric equilibrium is obtained) has been studied. An empirical prediction for the accessibility of the reconnected state is given. In particular, tearing modes with low poloidal mode number (m = 2, 3) are considered in order to interpret some minor disruptions observed in tokamaks, i.e. m = 3 minor disruptions in the Princeton Large Torus. Tearing modes with higher poloidal mode number have also been examined