Average yrast moments of inertia at high spins, where the pairing correlations are expected to be largely absent, were found to deviate from the rigid‐body values. This indicates that shell effects contribute to the moment of inertia. We discuss the gross dependence of moments of inertia and shell energies on the neutron number in terms of the semiclassical periodic orbit theory. We show that the ground‐state shell energies, nuclear deformations and deviations from rigid‐body moments of inertia are all due to the same periodic orbits. © 2003 American Institute of Physics