By applying a hydrodynamic representation of nonrelativistic scalar electrodynamics to the superconducting order parameter, we predict a negative (attractive) pressure between planar superconducting bodies. For con- ventional superconductors with London penetration depth λL ≈ 100 nm, the pressure reaches tens of N/mm2 at angstrom separations. The resulting surface energies are in better agreement with experimental values than those predicted by the Hartree-Fock theory, and the emergent electric-field screening length is comparable to that of the Thomas-Fermi theory. The model circumvents the bulk limitations of the Bardeen-Cooper-Schrieffer and Ginzburg-Landau theories to the analysis of superconducting quantum devices.