Formation and field-induced behavior of the equilibrium domain structure in the easy-plane antiferromagnets (AFM) with a strong magnetoelastic coupling is considered in a framework of phenomenological model. The surface of AFM is considered as a peculiar phase with its own magnetic and elastic properties different from those of the bulk. The incompatibility between the surface and the bulk strains arising in the course of the AFM phase transition is treated as a source of elastic \"charges\"that produce a long-range Coulomb-like \ßtray field\"which is responsible for the formation and reconstruction of the domain structure in the absence of magneto¯dipole interactions.