  We study the problem of flux penetration into type--I superconductors with
high demagnetization factor (slab geometry).Assuming that the interface between
the normal and superconducting regions is sharp, that flux diffuses rapidly in
the normal regions, and that thermal effects are negligible, we analyze the
process by which flux invades the sample as the applied field is increased
slowly from zero.We find that flux does not penetrate gradually.Rather there is
an instability in the process and the flux penetrates from the boundary in a
series of bursts, accompanied by the formation of isolated droplets of the
normal phase, leading to a multiply connected flux domain structure similar to
that seen in experiments.
