Abstract: Static and dynamic stabilities of clamped-clamped fluid pipes are investigated. The pipes rest on Pasternak-type two-parameter elastic foundations. Applying the complex mode method, the natural frequencies and critical flow velocity are calculated. For the case of pulsating inner flow, regions of principal parametric resonances for the first two modes and the combination resonance are obtained using the averaging method. The contributions of the linear and sheer foundation rigidities as well as some pipe parameters on the stabilities of the system are discussed. The results demonstrate that the variation of foundation rigidities can influence both the static and dynamic stabilities, and the effect of the sheer rigidity is much greater than that of the linear rigidity and can’t be neglected; moreover, some pipe parameters such as tension force, mass ratio of fluid to pipe, viscoelastic coefficient and mean flow velocity have some impacts on the stabilities of the system.