The stability of a simply supported straight pipe is investigated. The time dependent flow is assumed to vary harmonically about a constant mean velocity. Stability conditions and dynamic reponses of a governing equation are conducted by use of multiple scale mettled. Parametric resonances and combination resonances are investigated. Stability boundaries are analytically determined. The resulted stability conditions show that instabilities exist when the frequency of flow fluctuation is close to two times the natural frequency or to the sum of any two natural frequencies. In case that the fluctuated flow frequency is close to zero or to the difference of two natural frequencies, however, instabilities are not found up to the first order of perturbation. Stability charts are numerically Presented fir the first two vibration modes.