An exactly solvable model for the magnetostriction (MS) of a granular superconductor is presented. Both the bulk-modulus-driven magnetostriction'' (the change of the sample's volume in the magnetic free energy upon the applied stress) and the change-of-phase magnetostriction'' (due to the stress dependence of the weak-links-induced magnetization) are considered. It is found that the former contribution to MS dominates at small magnetic fields (in a Meissner phase of granular superconductor) while the latter one prevails at higher fields when the motion of Josephson vortices over grain boundaries is established. A useful link between MS and grain-boundary-pinning ability is obtained within the model. From magnetostriction measurements, this allows one to get rather unique information on the temperature and magnetic-field dependence of the weak-link pinning-force density and its field derivative. Analogy with the behavior of MS in the mixed state of type-II superconductors is stressed, and comparison of the model predictions with some experimental data on high-[ital T][sub [ital c]] ceramics is discussed.