The behavior of standing wave accelerator tanks, made up of chains of resonant cavities, is investigated using a coupled resonator model. This model gives accurate predictions of the behavior of such a cavity chain, including tolerances to errors in manufacture, cavity feed distributions, and transient response. The parameters necessary in the theory, the cavity couplings, Q's, and frequencies, may easily be determined by experiment. Extension of the simple chain to a more complex chain with double periodicity and second nearest neighbor coupling is demonstrated. Advantages of operating such accelerators in the &pgr;/2 mode are shown.