During branching morphogenesis, a simple cluster of cells proliferates and branches to generate an arborized network that facilitates fluid flow. The overall architecture of the mouse lung is established by domain branching, wherein new branches form laterally off the side of an existing branch. The airway epithelium develops concomitantly with a layer of smooth muscle that is derived from the embryonic mesenchyme. Here, we examined the role of smooth muscle differentiation in shaping emerging domain branches. We found that the position and morphology of domain branches are highly stereotyped, as is the pattern of smooth muscle that differentiates around the base of each branch. Perturbing the pattern of smooth muscle differentiation genetically or pharmacologically causes abnormal domain branching. Loss of smooth muscle results in ectopic branching and decreases branch stereotypy. Increased smooth muscle suppresses branch initiation and extension. Computational modeling revealed that epithelial proliferation is insufficient to generate domain branches and that smooth muscle wrapping is required to shape the epithelium into a branch. Our work sheds light on the physical mechanisms of branching morphogenesis in the mouse lung.