The concept of structured singular value was recently introduced by Doyle (Proc. IEE, vol. 129, pp. 242-250, 1982) as a tool for the analysis and synthesis of feedback systems with structured uncertainties. In this paper an equivalent expression for the structured singular value is proposed, leading to an alternative algorithm for its computation. The new approach is based on the geometric properties of the generalized numerical range of certain matrices. Similar to previously considered schemes, the algorithm proposed here is proven to give the correct value for block-structures of size up to 3. For larger sizes, insight is gained in the question of the possible 'gap' between the structured singular value and its known upper bound.