In previous articles (Dupraz & Combes, 1985, 1986a), we showed that shells form with different geometries around prolate and oblate galaxies. However, theory and observations suggest that some ellipticals could be tumbling bars (Miller & Smith 1980; Müllenhoff & Marenbach 1986). Here we simulate the accretion of a small galaxy by a tumbling bar; the tumble period T& is kept free. Let Tp be the typical period of motion of a particle in the potential of the elliptical galaxy. Then we find (Dupraz & Combes, 1986b):

a) When Tt > 3TP (Figure l a), shells form with the geometry of a static prolate potential, i.e., aligned with the major axis.

When Tb < 3Tp (Figure lc), the particles feel the time-averaged potential, which is oblate: the shells display the typical oblate geometry. But there is no confusion with a static oblate shell galaxy, because the tumbling bars must be seen edge -on for the shells to appear.

c) When Tb ~ 3Tp (Figure lb), the outer shells form with the oblate geometry, the inner shells with the prolate geometry. In between, no shells form, because particles follow resonant (non-radial) motions.