Tissue folding is a fundamental process occurring often in animal organ development. Here, we study the progression of fold shape and the underlying mechanics in the development of the Drosophila wing disc. We present a 3D segmentation of the apical surface of the wing disc proper from larval stages, when folds grow, to early pupariation, when the tissue unfolds and remodels into a bilayer. We establish morphological metrics to quantify and resolve fold shape in this dataset, introducing a definition of fold depth and width that can be used to characterize folds on a curved surface. Furthermore, we identify fibrous extracellular matrix on the apical side (aECM) that physically connects the two opposing sides of the folds. By modeling a tissue fold with a lateral vertex model endowed by an adhesive layer representing the aECM, we predict that unfolding in the wing disc is preceded by the removal of aECM. Using genetic perturbations, we confirm that aECM adhesion affects fold stability and mechanics: loss of aECM leads to abnormal fold shape and unfolding dynamics, whereas failure to remove aECM at pupariation inhibits unfolding. Finally, we show that these aECM perturbations in larval stages cause morphological phenotypes in the adult wing, demonstrating that the fold morphology of the wing disc helps to define adult wing shape. In total, our work establishes a key mechanical role for aECM in wing disc growth and morphogenesis and advances our general understanding of how epithelial tissue folds can be mechanically stabilized during development.