A model of the elongation of P pili expressed by uropathogenic Escherichia coli exposed to stress is presented. The model is based upon the sticky chain concept, which is based upon Hooke's law for elongation of the layer-to-layer and head-to-tail bonds between neighboring units in the PapA rod and a kinetic description of the opening and closing of bonds, described by rate equations and an energy landscape model. It provides an accurate description of the elongation behavior of P pili under stress and supports a hypothesis that the PapA rod shows all three basic stereotypes of elongation/unfolding: elongation of bonds in parallel, the zipper mode of unfolding, and elongation and unfolding of bonds in series. The two first elongation regions are dominated by a cooperative bond opening, in which each bond is influenced by its neighbor, whereas the third region can be described by individual bond opening, in which the bonds open and close randomly. A methodology for a swift extraction of model parameters from force-versus-elongation measurements performed under equilibrium conditions is derived. Entities such as the free energy, the stiffness, the elastic elongation, the opening length of the various bonds, and the number of PapA units in the rod are determined.