An efficient numerical method for examining the stability of linear time varying systems modeled by finite element (FE) methods is presented in this paper. Parametric instability of pipes conveying pulsating fluid flow is studied using multivariable Floquet-Lyapunov theory. In order to solve large size problems, the system matrices are reduced to a smaller size by transforming to modal coordinates using modal vectors. This transformation preserves the stability information and the reduced matrix is used for the evaluation of the monodromy matrix. For dealing with large systems with parametric excitations, it is found that proposed method is numerically efficient. © 2003 Elsevier B.V. All rights reserved.