  We calculate the elongation or contraction force $F$ on a point contact
(length $L$) connecting two superconductors with a phase difference $\phi$.
When $L$ is small compared to the superconducting coherence length $\xi_0$ this
force is given by $F=-(\Delta_0/\pi\xi_0)\ln(\xi_0/L)\cos\phi$ per
spin-degenerate transverse mode. Quantum fluctuations in states from the
continuous spectrum outside the superconducting gap $\Delta_0$ give the
dominant contribution to this force, which may be understood as the
superconducting counterpart of the electromagnetic Casimir force. We compare
with earlier work that only included contributions from the discrete spectrum
of Andreev levels.
