The vertebrate unfolded protein response (UPR) is characterized by multiple interacting nodes among its three pathways, yet the logic underlying this regulatory complexity is unclear. To begin to address this issue, we created a computational model of the vertebrate UPR that was entrained upon and then validated against experimental data. As part of this validation, the model successfully predicted the phenotypes of cells with lesions in UPR signaling, including a surprising and previously unreported differential role for the eIF2α phosphatase GADD34 in exacerbating severe stress but ameliorating mild stress. We then used the model to test the functional importance of a feedforward circuit within the PERK/CHOP axis and of cross-regulatory control of BiP and CHOP expression. We found that the wiring structure of the UPR appears to balance the ability of the response to remain sensitive to endoplasmic reticulum stress and to be deactivated rapidly by improved protein-folding conditions. This model should serve as a valuable resource for further exploring the regulatory logic of the UPR.