We treat layers of sedimentary rock as elastic plates and predict the orientations of joints by assuming that they open parallel to the maximum instantaneous stretch of a layer. Because the direction of maximum instantaneous stretch is parallel to the maximum curvature of a surface, we hypothesize that joints will trend parallel to the minimum curvature of an elastically deformed layer. After constructing pseudo–three-dimensional trishear models of Laramide-style uplifts that grow self-similarly, we calculated the direction of minimum-curvature axes during the evolution of the fold. Our analysis of minimum-curvature axes in evolving folds suggests several important characteristics for fold-related joint sets: (1) joints that are neither parallel nor perpendicular to the fold axis may be induced by local fold-related strains; (2) at any time during folding, joint orientations may vary according to the structural position on a fold; (3) at any location on a fold, joint orientation may depend on when a joint forms during the evolution of the fold; and (4) joint patterns in trishear folds may vary with stratigraphic position. Natural folds that evolve along simple geometric pathways may develop fold-related joint sets, the orientation, dominance, abutting relationships, spacing, and continuity of which will vary systematically throughout the structure. This variation in joint-system architecture may reflect the history of fold growth.