The branched patterns of epithelial organs are generated by spatial differences in the behaviors of individual cells. In addition to biochemical gradients, cells within branching tissues are possibly exposed to mechanical gradients that originate both internally and externally. We have developed lithography-based three-dimensional culture models that recapitulate the architecture of mammary epithelial trees; these engineered tissues undergo a morphogenesis process similar to that of the mammary gland in vivo. Here we combine these models with computational approaches to investigate the role of external and internal mechanical stress gradients during tissue development. We characterize the effects of cell contractility, intercellular adhesion and extracellular matrix stiffness on the emergent pattern and extent of branching in mammary epithelium. Our data provide physical understanding of the morphogenetic processes that drive normal tissue development, and can help elucidate the events that lead to pathologies such as fibrosis and tumorigenesis.