A finite-element approach for the eigenmode analysis of open resonators is presented using a perfectly matched layer (PML) absorbing boundary condition. The PML is a nonphysical anisotropic lossy material absorbing outgoing waves from the computational domain. The validity of the approach is examined via the application to a Fabry-Perot resonator problem. Numerical error analyses for the quality factors and resonant frequencies demonstrate the accuracy and reliability of the anisotropic PML method applied to the eigenvalue problem. (C) 1997 John Wiley & Sons, Inc.