  We use a perturbative semiclassical trace formula to calculate the three
lowest-order multipole (quadrupole $\eps_2$, octupole $\eps_3$, and
hexadecapole $\eps_4$) deformations of simple metal clusters with $90 \le N \le
550$ atoms in their ground states. The self-consistent mean field of the
valence electrons is modeled by an axially deformed cavity and the oscillating
part of the total energy is calculated semiclassically using the shortest
periodic orbits. The average energy is obtained from a liquid-drop model
adjusted to the empirical bulk and surface properties of the sodium metal. We
obtain good qualitative agreement with the results of quantum-mechanical
calculations using Strutinsky's shell-correction method.
