The axisymmetric electrohydrodynamic deformation of an elastic capsule with a capacitive membrane obeying the Skalak law under a uniform AC electric field is investigated using analytical and boundary integral theory. The low capillary number (the ratio of destabilizing shear or electric force to the stabilizing elastic force) regime shows that time-averaged prolate and oblate spheroid deformations, and the time-periodic prolate–sphere, oblate–sphere breathing modes are commensurate with the time averaged-deformation. A novel prolate–oblate breathing mode is observed due to an interplay of finite membrane charging time and the field reversal of the AC field. The study, when extended to high capillary numbers, shows new breathing modes of cylinder–prolate, cylinder–oblate, and biconcave–prolate deformation. These are the results of highly compressive normal Maxwell stress at the poles and are aided by a weak compressive equatorial stress, characteristic of a capacitive membrane. The findings of this work should form the basis for the understanding of more complex biological cells and synthetic capsules for industrial applications.