The formation of epithelial tubes is essential to build organs responsible to direct vital factors outside-in, inside-out or within a living animal (e.g., food and water in the gut, air in the lungs, saliva from salivary-tubes, blood in blood-vessels etc.). Therefore, tube formation plays a critical role in multicellular life organized in stratified layers where an inside and an outside are established. Understanding the mechanisms and mechanics responsible for tube formation is thus key to understand the emergence of complex life forms. Tube formation can result from tissue in- pocketing: the bending of a tissue patch forming a pocket like shape. The mechanisms responsible for in-pocketing are not well understood. To dissect and study this process we use the sea urchin Paracentrotus lividus embryo, a quite simple and powerful model system ideal for in vivo mechanical studies. We are focused in better understanding the formation of the archenteron during the sea urchin embryo gastrulation: a tubular epithelial structure that eventually forms the gut of the sea urchin larva. Our work highlights a combination of coordinated and radially planar cell polarized mechanisms that are responsible for simultaneous folding and extension of the embryo vegetal plate during the primary phase of tissue in-pocketing. By implementing infra-red femtosecond ablation coupled to 4D multi-view light sheet microscopy, drug and RNAi perturbation, μ-aspiration and indentation to measure tissue mechanical properties, in toto 4D segmentation and mathematical modelling, this work shines new light on the mechanisms and mechanics initiating tissue in-pocketing for tube formation and embryo gastrulation.