When a laser pulse impinges on a molecule which is invariant under certain symmetry operations selection rules for harmonic generation (HG) arise. In other words, symmetry controls which channels are open for the deposition and emission of laser energy—with the possible application of filtering or amplification. We review the derivation of HG selection rules and study numerically the interaction of laser pulses with an effectively one-dimensional ring-shaped model molecule. The harmonic yields obtained from that model and their dependence on laser frequency and intensity are discussed. In a real experiment obvious candidates for such molecules are benzene, other aromatic compounds, or even nanotubes.