Vertebrate neural tube formation involves two distinct morphogenetic events--convergent extension (CE) driven by mediolateral cell intercalation, and bending of the neural plate driven largely by cellular apical constriction. However, the cellular and molecular biomechanics of these processes are not understood. Here, using tissue-targeting techniques, we show that the myosin IIB motor protein complex is essential for both these processes, as well as for conferring resistance to deformation to the neural plate tissue. We show that myosin IIB is required for actin-cytoskeletal organization in both superficial and deep layers of the Xenopus neural plate. In the superficial layer, myosin IIB is needed for apical actin accumulation, which underlies constriction of the neuroepithelial cells, and that ultimately drive neural plate bending, whereas in the deep neural cells myosin IIB organizes a cortical actin cytoskeleton, which we describe for the first time, and that is necessary for both normal neural cell cortical tension and shape and for autonomous CE of the neural tissue. We also show that myosin IIB is required for resistance to deformation ("stiffness") in the neural plate, indicating that the cytoskeleton-organizing roles of this protein translate in regulation of the biomechanical properties of the neural plate at the tissue-level.