  The random-phase-approximation (RPA) method with separable residual forces
(SRPA) is proposed for the description of multipole electric oscillations of
valence electrons in deformed alkali metal clusters. Both the deformed mean
field and residual interaction are derived self-consistently from the Kohn-Sham
functional. SRPA drastically simplifies the computational effort which is
urgent if not decisive for deformed systems. The method is applied to the
description of dipole, quadrupole and octupole plasmons in deformed sodium
clusters of a moderate size. We demonstrate that, in clusters with the size
N>50, Landau damping successfully competes with deformation splitting and even
becomes decisive in forming the width and gross structure of the dipole
plasmon. Besides, the plasmon is generated by excitations from both ground
state and shape isomers. In such clusters familiar experimental estimates for
deformation splitting of dipole plasmon are useless.
