The linearized Vlasov equation gives a semiclassical version of the ra
ndom phase approximation. The solution of this equation is studied for
electrons moving in a deformed equilibrium mean field which is approx
imated by a cavity of a. spheroidal shape (both prolate and oblate). C
ontrary to spherical systems, there is a coupling between excitations
of different multipolarity induced by the interaction between constitu
ents. The dipole response presents a typical double-peaked profile wit
h a strong dependence on the deformation.