Ball lightning (BL) is mathematically modelled assuming a solid, positively charged core exists at its center. The large amount of energy occassionally associated with BL is mainly due to the electrostatic (ES) energy of the charge on the core. The upper energy limit is determined by the size and strength of the core and this energy can be orders of magnitude greater than the energy which can be confined by atmospheric pressure alone. A pure electron layer and a plasma layer surround the core. The charge of the electron layer is equal in magnitude to that of the core. An electormagnetic (EM) field is completely trapped by the electron and plasma layers. The electron temperature is sufficiently high that absorption by electron-ion collisions is small, enabling the ball to have a lifetime of seconds or more. The ponderomotive force (radiation pressure) of the trapped EM field balances the ES force of the electrons toward the core plus the force of atmospheric pressure. The generation mechanism is not considered. ¿American Geophysical Union 1990