The budding of tubular organs from flat epithelial sheets is a vital morphogenetic process. Cell behaviours that drive such processes are only starting to be unraveled. Using live-imaging and novel morphometric methods, we show that in addition to apical constriction, radially oriented directional intercalation of cells plays a major contribution to early stages of invagination of the salivary gland tube in the Drosophila embryo. Extending analyses in 3D, we find that near the pit of invagination, isotropic apical constriction leads to strong cell-wedging. Further from the pit cells interleave circumferentially, suggesting apically driven behaviours. Supporting this, junctional myosin is enriched in, and neighbour exchanges are biased towards the circumferential orientation. In a mutant failing pit specification, neither are biased due to an inactive pit. Thus, tube budding involves radially patterned pools of apical myosin, medial as well as junctional, and radially patterned 3D-cell behaviours, with a close mechanical interplay between invagination and intercalation.