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 ϕ and χ1 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 Cγ-Cδ-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.