In proteins, the proline ring exists predominantly in two discrete states. However, there is also a small but significant amount of flexibility in the proline ring of high-resolution protein structures. We have found that this side-chain flexibility is coupled to the backbone conformation. To study this coupling, we have developed a model that is simply based on geometric and steric factors and not on energetics. We show that the coupling between phi and chi1 torsions in the proline ring can be described by an analytic equation that was developed by Bricard in 1897, and we describe a computer algorithm that implements the equation. The model predicts the observed coupling very well. The strain in the C(gamma)-C(delta)-N angle appears to be the principal barrier between the UP and DOWN pucker. This strain is relaxed to allow the proline ring to flatten in the rare PLANAR conformation.