Diverse types of epithelial morphogenesis drive development. Similar cytoskeletal and cell adhesion machinery orchestrate these changes, but it is unclear how distinct tissue types are produced. Thus, it is important to define and compare different types of morphogenesis. We investigated cell flattening and elongation in the amnioserosa, a squamous epithelium formed at Drosophila gastrulation. Amnioserosa cells are initially columnar. Remarkably, they flatten and elongate autonomously by perpendicularly rotating the microtubule cytoskeleton--we call this 'rotary cell elongation'. Apical microtubule protrusion appears to initiate the rotation and microtubule inhibition perturbs the process. F-actin restrains and helps orient the microtubule protrusions. As amnioserosa cells elongate, they maintain their original cell-cell contacts and develop planar polarity. Myosin II localizes to anterior-posterior contacts, while the polarity protein Bazooka (PAR-3) localizes to dorsoventral contacts. Genetic analysis revealed that Myosin II and Bazooka cooperate to properly position adherens junctions. These results identify a specific cellular mechanism of squamous tissue morphogenesis and molecular interactions involved.