The Gamma Knife is a highly specialized treatment unit that provides an advanced stereotactic approach to the treatment of tumors, vascular malformations, and pain disorders within the head. Inside a shielded treatment unit, beams from 201 radioactive sources are focused so that they intersect at the same location in space, resulting in a spherical region of high dose referred to as a shot of radiation. The location and width of the shots can be adjusted using focussing helmets. By properly combining a set of shots, larger treatment volumes can be successfully treated with the Gamma Knife. The goal of this project is to automate the treatment planning process. For each patient, an optimization seeks to produce a homogeneous dose distribution that conforms closely to the treatment volume, while avoiding overdosing nearby sensitive structures. The variables in the optimization can include the number of shots of radiation along with the size, the location, and the weight assigned to each. Formulation of such problems using a variety of mathematical programming models is described, and the solution of several test and real-patient examples is demonstrated. This represents joint work with: David M. Shepard Department of Radiation Oncology, University of Maryland School of Medicine, 22 South Green Street, Baltimore, MD 21201 email: dshep001@umaryland.edu