In the present work the fluid-structure interaction is analysed for compliant piping systems by assuming a linear viscoelastic behavior of the pipe material. The effects of pipe motion on transient responses of liquid pressure and pipe stresses are theoretically investigated when the system is disturbed in some fashion such as rapid valve closure and an external impact load. In this analysis it is considered the wave propagation process in the pipe wall due to localized hidrodynamics efforts and the Poisson effect. The set of equations describing the dynamics of the liquid and pipe wall are coupled and solved numerically by means of the method of characteristics. The results obtained for some piping systems are compared with those observed for elastic pipe material and with experiments available in the literature. The results indicate that the structural motion can produce pressures and stresses higher than those predicted by the classical, uncoupled, waterhammer analysis, particularly at the begining of the transient, before pipe material viscoelasticity damps the system responses. However, the increase observed on pressures and stresses due to structural motion is not as significant for a viscoelastic pipeline as it is for an elastic pipe.