The shell correction method is applied to calculate the shapes and bin
ding energies of Na clusters. The axial equilibrium shapes are calcula
ted by minimizing five deformation parameters simultaneously. Strong d
eviations from spheroidal shapes including reflection asymmetric ones
are found. The influence of cluster deformation on the separation ener
gies and ionization potentials and on the splitting of the photo - res
onance are compared with the available experimental data. The N-depend
ence of the cluster shape and its relation to the N- and Z-dependences
of the nuclear shape is discussed.