Many biological structures are curved. Here we use a Lagrangian analysis of growth (following tissue elements to determine how their expansions and growth displacements change as a function of time and position) to reveal how spatio-temporal patterns of growth can set up mechanical stresses that drive the production of ruffles in a biological structure in response to environmental.cues. Nereocystis luetkeana , abundant nearshore kelp, have wide ruffled blades that minimize self-shading in slow flow, but narrow flat blades that reduce hydrodynamic drag in rapid flow. Previously we showed that blade ruffling is a plastic trait associated with a transverse gradient in longitudinal growth. Here we consider both expansion of tissue elements and their displacements due to growth in blades and find that growth patterns regulating ruffle formation are induced by tensile stress due to hydrodynamic drag, but not by shading or nutrient levels. When longitudinal stress in a blade is low in slow flow, blade edges grow faster than the midline in young tissue near the blade base. Tissue elements are displaced distally by expansion of younger proximal tissue. As predicted by elasticity theory, strain energy caused by the transverse gradient in longitudinal growth is not released by elastic buckling until the blade grows wide and thin enough, producing ruffles distal to the region where the growth inhomogeneity was initiated. If a blade experiences higher stress in rapid flow, edges and midline grow at the same rate, so the blade becomes flat as these new tissue elements are displaced distally.