This paper presents some results on the analysis of coupled vibration of a thin cylindrical pipe containing a flewing flind. A simple formula is ob- tained by means of which one can compute the lower natural frequencies of vibration when the flow velocity is sufficiently low. This paper presents some results on the analysis of coupled vibration of a thin cylindrical pipe containing a flewing flind. A simple formula is ob- tained by means of which one can compute the lower natural frequencies of vibration when the flow velocity is SUTIL LOW.