Multileaf collimators have become available in many radiotherapy treatment centres. The cross section of a beam can be shaped to a projection of the target area by moving the leaves of the multileaf collimator into the beam. In this paper, a method is described to optimize the positions of the individual leaves automatically, once the beam directions and weights have been chosen. The individual positions of the leaves are optimized using the variable metric method. Changes in dose resulting from small leaf movements are computed efficiently using a special method. The optimization method was tested on a treatment plan for a phantom patient. It was found that the unnecessary edges of the beams were trimmed efficiently.