The results of numerical calculations of A* for a class of equilibria typical of those encountered during the early formation stage of the SI Spheromak are presented. The equilibrium plasma is assumed to be cylindrically symmetric and pressureless. It encloses a current-carrying perfect conductor (flux core) and is surrounded by a vacuum with zero longitudinal field. Stability boundaries in the space formed by the equilibrium parameters are mapped. The plasma is tearing-mode-stable provided BzBg at the flux core is below a certain critical value which depends on the equilibrium parameters. For typical equilibria this critical value is 0.65. © 1982 IOP Publication Ltd.