A self-consistent mean-field lattice gas theory of intercalation compounds is proposed in which effective interactions between interstitials are described by short-range screened Coulomb repulsions and long-range attractions due to elasticity of the host matrix. Depending on the relative strength of elastic interactions, the phase diagram contains domains of the first- and second-order transitions of the order-disorder type, separated by a tricritical line, and the domain of a "gas-liquid" transition separated from the homogeneous state by a critical line. These features give rise to different types of behavior of the open circuit voltage (OCV) of a rechargeable battery in which an intercalation compound is used as an electrode material. Theoretical predictions are compared with experiment.