An equilibrium theory of the length of intense electron bunches circulating in a storage ring is presented. The consequence of electrical interaction with various resonant structures is expressed in terms of quadratures over the impedance of the structures, and impedance functions for a variety of elements are evaluated. It is shown that elements having resonances at high frequency can, above transition, cause bunches to increase in length with increasing current. The parametric dependence of the bunch lengthening is found to be in good agreement with observations, and numerical estimates, which are in substantial agreement with experiment, are presented.