It is shown that a charged spherically symmetric star, made out of a c
ontinuous superposition of thin shells with Poincare stresses, undergo
es gravitational collapse in free fall like an uncharged star of dust.
The interior solution is a Friedmann universe matching the Reissner-N
ordstrom geometry at the boundary of the star. When the absolute value
of the charge Q does not exceed the mass M, the star rebounds elastic
ally inside the event horizon at the radial coordinate Q2/(2M). The fu
rther history of the charged star after the bounce is analyzed. Beside
s, a simple mechanism which accounts for the development of Poincare s
tresses in an originally charged star of dust is suggested. It is also
verified that the energy density is nonnegative all along the collaps
e process.