The first event of Drosophila gastrulation is the formation of the ventral furrow. This process, which leads to the invagination of the mesoderm, is a classical example of epithelial folding. To understand better the cellular changes and dynamics of furrow formation, we examined living Drosophila embryos using three-dimensional time-lapse microscopy. By injecting fluorescent markers that visualize cell outlines and nuclei, we monitored changes in cell shapes and nuclear positions. We find that the ventral furrow invaginates in two phases. During the first ‘preparatory’ phase, many prospective furrow cells in apparently random positions gradually begin to change shape, but the curvature of the epithelium hardly changes. In the second phase, when a critical number of cells have begun to change shape, the furrow suddenly invaginates. Our results suggest that furrow formation does not result from an ordered wave of cell shape changes, contrary to a model for epithelial invagination in which a wave of apical contractions causes invagination. Instead, it appears that cells change their shape independently, in a stochastic manner, and the sum of these individual changes alters the curvature of the whole epithelium.