We demonstrate that in the zebrafish hindbrain, cell shape, rhombomere morphogenesis and, unexpectedly, brain ventricle lumen expansion depend on the contractile state of the neuroepithelium. The hindbrain neural tube opens in a specific sequence, with initial separation along the midline at rhombomere boundaries, subsequent openings within rhombomeres and eventual coalescence of openings into the hindbrain ventricle lumen. A mutation in the myosin phosphatase regulator mypt1 results in a small ventricle due to impaired stretching of the surrounding neuroepithelium. Although initial hindbrain opening remains normal, mypt1 mutant rhombomeres do not undergo normal morphological progression. Three-dimensional reconstruction demonstrates cell shapes within rhombomeres and at rhombomere boundaries are abnormal in mypt1 mutants. Wild-type cell shape requires that surrounding cells are also wild type, whereas mutant cell shape is autonomously regulated. Supporting the requirement for regulation of myosin function during hindbrain morphogenesis, wild-type embryos show dynamic levels of phosphorylated myosin regulatory light chain (pMRLC). By contrast, mutants show continuously high pMRLC levels, with concentration of pMRLC and myosin II at the apical side of the epithelium, and myosin II and actin concentration at rhombomere boundaries. Brain ventricle lumen expansion, rhombomere morphology and cell shape are rescued by inhibition of myosin II function, indicating that each defect is a consequence of overactive myosin. We suggest that the epithelium must `relax', via activity of myosin phosphatase, to allow for normal hindbrain morphogenesis and expansion of the brain ventricular lumen. Epithelial relaxation might be a widespread strategy to facilitate tube inflation in many organs.