Organs are sculpted by extracellular as well as cell-intrinsic forces, but how collective cell dynamics are orchestrated in response to environmental cues is poorly understood. Here we apply advanced image analysis to reveal extracellular matrix-responsive cell behaviors that drive elongation of the Drosophila follicle, a model system in which basement membrane stiffness instructs three-dimensional tissue morphogenesis. Through in toto morphometric analyses of wild type and round egg mutants, we find that neither changes in average cell shape nor oriented cell division are required for appropriate organ shape. Instead, a major element is the reorientation of elongated cells at the follicle anterior. Polarized reorientation is regulated by mechanical cues from the basement membrane, which are transduced by the Src tyrosine kinase to alter junctional E-cadherin trafficking. This mechanosensitive cellular behavior represents a conserved mechanism that can elongate edgeless tubular epithelia in a process distinct from those that elongate bounded, planar epithelia.