Spheroidal nuclear vibrations are considered using a macroscopic model
based on the assumption that nuclear matter possesses the properties
of elastic medium. Emphasis is laid on the analysis of instability of
the quadrupole configuration. It is presumed that the onset of this in
stability is associated with the commencement of fission. The proposed
fluid-dynamics model predicts the values of the parameters of nuclear
fission that differ somewhat from the values given by the standard li
quid drop-model. In particular, the obtained critical ratio Z2/A, whic
h characterizes the loss of stability of the quadrupole mode, is equal
to 35. It follows from this estimate that fission induced by an exter
nal perturbation should be expected for nuclei (from the beta-stabilit
y valley) with A greater-than-or-equal-to 230.