Zero-temperature field-induced polarization, supercurrent density, and the related electrostriction (ES) of a granular superconductor are calculated within a model of 3D Josephson junction arrays. Both the "bulk-modulus-driven ES" (the change of the sample's volume in the free energy upon the applied stress) and the "change-of-phase ES" (due to the stress dependence of the weak-links-induced polarization) are considered. In contrast to magnetostriction of a granular superconductor, its electroelastic behavior is predicted to be dominated by the former contribution for all applied fields.(June 3, 2013)Some attention was given recently to rather peculiar electric-field induced phenomena, either observed experimentally (like a substantial critical current enhancement [1-3]) or predicted to occur (like a possibility of magnetoelectric effect due to the DzyaloshinskiMoria type coupling between an applied electric field and an effective magnetic field of circulating Josephson currents [4]) in granular superconductors and attributed to their weak-link structure. At the same time, as compared to the magnetoelastic behavior of superconducting materials (dominated either by a vortex response [5][6][7][8] or by weak-links structure [9]), their electroelastic behavior still remains to be properly addressed.In the present communication, another interesting pnenomenon related to the modification of the sample's weak-links structure in an applied electric field is discussed. Namely, we consider a possible role of Josephson junctions in low-temperature behavior of the fieldinduced polarization and the related electroelastic properties of granular superconductors.As is well-known [10], the change of the free energy of a superconductor in the presence of an external electric field E readswhere P (E) is the electric polarization of a granular superconductor at zero temperature (see below), V its volume, and the internal field E i is related to the applied field E via an effective dielectric constant ǫ, namely [10] E i = E/ǫ. When a superconductor is under the influence of an external (homogeneous) stress σ, the above free energy results in the associated strain component (in what follows, we consider only a strain component U normal to the applied electric field E)Neglecting a possible change of the effective dielectric constant ǫ with the stress, Eqs. (1) and (2) give rise to the following two main contributions to the electrostrictive (ES) strains, namely (a) the "bulk-modulus-driven ES" due to the change in the free energy arising from the stress dependence of the sample volume (3) (b) the "change-of-phase ES" due to the stress dependence of the polarization via the Josephson junction effective surface (see below)To proceed, we need an explicit form of the induced polarization P (E). And to this end, we employ the model of a granular superconductor based on the well-known tunneling Hamiltonian (see, e.g., Ref.[11])where φ ij (t) = φ ij (0) + ω ij ( E)t,withand φ ij (0) = φ i − φ j , r ij = r i − r j ,1