Abstract: As the third paper in this series of nonlinear applications of the finite element method of lines (FEMOL), the present paper applies this method to eigenvalue problems by presenting a FEMOL analysis of the free vibration of various membranes. Firstly, the vibration problem is discretized into eigenvalue problem in ODEs. Then using a number of ODE conversion techniques, the eigenvalue problem is further transformedinto a standard nonlinear ODE problem, which is solved by a recently -developed ODE eigen-solver. Numerical examples are given to show the present approach.