We measure Young's modulus of a free polyelectrolyte multilayer film by studying osmotically induced swelling of polyelectrolyte multilayer microcapsules filled with the polyelectrolyte solution. Different filling techniques and core templates were used for the capsule preparation. Varying the concentration of the polyelectrolyte inside the capsule, its radius and the shell thickness yielded an estimate of Young's modulus of the order of 100 MPa. This corresponds to an elastomer and reflects strong interactions between polyanions and polycations in the multilayer.