We have studied the mechanisms whereby a strong electric shock terminates chaotic wave propagation in cardiac tissue (defibrillation). In a generic model of cellular excitable tissue with two variables, we have found two mechanisms: one based on excitation (E), and another based on de-excitation (D) of cells by the small scale periodic component of transmembrane potential induced by the shock. Symmetry properties of the current-voltage characteristics describing the dynamics of the fast ionic currents, along with the strength of the electric field determine which of these mechanisms operates. A prediction of this work to be tested experimentally is that upon increasing the electric field one mechanism may switch to another, resulting in the following unusual sequence of events: defibrillation is first possible by mechanism E at moderate fields, then impossible, and finally possible by mechanism D, at higher fields.