The existence of closed shells in nuclei is indicated by the particular stability and abundance of nuclear systems with certain numbers of neutrons and of protons. An interesting correspondence exists between these numbers and the degeneracy of energy levels in the model of free particles in a simple rectangular potential well. The empirical relations suggest the addition of a central depression to the well for light nuclei ($N$ or $Z\ensuremath{\leqq}20$) and a central elevation (Elsasser's wine bottle potential) for heavy nuclei. The qualitative physical explanation of these modifications is that for light nuclei, the particle density, and thus the nuclear interaction energy, is greatest at the center of the nucleus; for heavy nuclei, the Coulomb repulsion between protons produces a particle density varying from a minimum at the center to a maximum near the boundary, and therefore a similarly varying interaction energy. In the free particle model, levels with small angular momentum and nodes within the nucleus are displaced upward by the central elevation and crossing of levels in the desired direction occurs, though not exactly as required to explain the complete empirical list of closed shell numbers. It is apparent that a single particle model of the nucleus is an insufficient approximation; however qualitative arguments based on configuration interaction enable one to formulate, with little ambiguity, a shell model in agreement with the empirical facts.