The damping effects on stabilities of a simply supported pipe conveying fluid is investigated using the complexification-averaging method. The flow is assumed to vary harmonically about a mean speed. Unstable conditions of a piping system included with the viscous and material damping are analytically obtained for primary, secondary and combination parametric resonances. The primary and secondary resonances occur when the frequency of flow fluctuation is close to one and two times the natural frequency. And when this frequency is close to the sum of any two natural frequencies, combination resonances occur. The effects of damping parameters on the regions of three parametric resonances are discussed.