We extend a previous analysis of the buckling properties of a linear chain of hard spheres between hard walls under transverse harmonic confinement. Two regimes are distinguished—low compression, for which the entire chain buckles, and higher compression, for which there is localized buckling. With further increase of compression, second-neighbor contacts occur; beyond this compression the structure is no longer planar, and is not treated here. A continuous model is developed which is amenable to analytical solution in the low compression regime. This is helpful in understanding the scaling properties of both finite and infinite chains.