We generalize a recent study of the stability of isotropic (spherical) rota
ting membranes to the anisotropic ellipsoidal membrane. We find that while
the stability persists for deformations of spin l=1, the quadrupole and hig
her spin deformations (l greater than or equal to2) lead to instabilities.
We find the relevant instability modes and the corresponding eigenvalues. T
hese indicate that the ellipsoidal rotating membranes generically decay int
o fingerlike configurations.