SUMMARYA symmetric indirect Tre tz method is developed to solve the free vibration problem of a 2D membrane. It is proved that in this approach the spurious eigensolution exists, and an auxiliary matrix is constructed to help extraction of the spurious solution using the generalized singular-value decomposition. In addition to the spurious eigensolution, this regular formulation su ers from its ill-posed nature, i.e. the numerical instability. In order to deal with the numerical instability, the Tikhonov's regularization method, in conjunction with the generalized singular-value decomposition, is suggested. The proposed approach has some merits when compared with other regular boundary element formulations reported so far; namely the capacity of representing eigenmodes and the ability to deal with a multiply connected domain of genus 1. Several numerical examples are demonstrated to show the validity of the current approach.