Cancer radiotherapy, together with chemotherapy and surgery, form the basis of modern day cancer treatment. Its treatment pro- cess generally involves directing a high energy radiation beam at an identied cancerous growth from dierent directions and with varying beam shapes, durations, and intensities in order to kill the cancerous tissues while preserving nearby healthy ones. Volumetric modulated arc therapy comprises a recently developed setup using a full-rotation trajectory of the beam about the patient along with a multi-leaf collimator for beam shape sculpting. We introduce a variational model in this setup for the optimization of beam shapes and intensities while preserving certain constraints imposed by the equipment used. We apply a binary level-set strategy to represent beam shapes and a fast sweeping technique to satisfy beam intensity variation limits. The result is a ow-based shape optimization algorithm that guarantees constraint satisfaction and energy decrease for the generation of improved treatment plans in volumetric modulated arc therapy.