A computational method is presented for the analysis of interaction between a thin, flexible filament and wind flow around it. Restricting the computational domain to the two dimensional vertical plane, the filament is discretized by truss elements. A geometrically nonlinear dynamic analysis method is applied to the motion of the filament. The ALE finite element method is employed for the flow analysis. A simple staggered algorithm to solve the filament motion and the flow alternatively was unstable unless the density of the filament is sufficiently large. An improved algorithm, where the excessive acceleration of the filament due to the excessive fluid force is reduced by introducing an inner iteration algorithm during each time integration step, was found effective to simulate a wind-induced flutter of the filament stably.