A general finite element approach to computing the modes of open-boundary waveguides is presented. This efficient and robust scheme applies equally to situations with real and complex propagation constants. By using a localised boundary impedance condition, the approach preserves the sparsity of the global matrices. A comparison with the well established infinite element technique and the analysis of a 2-D leaky optical structure are given as examples. © 1994, IEE. All rights reserved.