Incremental harmonic balance method (IHBM) is applied to geometrically nonlinear vibration analysis of a simply supported pipe conveying fluid. the material of which is viscoelastic of the Kelvin- Voigt type. Some unstable phenomena - the appearance of the peak or jumps in the pipe's amplitude frequency curves, which are considered to be of importance to this kind of structure, are presented in the numerical results, and the influence of several parameters of the system on the dynamic characteristic of the pipe are also studied. It is believed that this is the first attempt to search for the periodic solution of the pipe and its intrinsic property with such a method.
