In this study, the natural frequency of a simply supported pipeline (hinged type) conveying one-dimension incompressible steady fluid flow set on viscoelastic foundation is investigated by using finite element analysis and the critical fluid velocity with different parameters such as stiffness and viscous coefficients of foundation are obtained. The foundation is simulated using the modified Winkler's model to introduce the effect of time dependent viscosity term. Some known results are confirmed and some new ones obtained. Two components of foundation, stiffness and viscosity, seemed to act on the critical flow velocity of the pipe in contrary trend. Where, increasing the foundation stiffness tended to increase the critical flow velocity in the pipe. While, increasing foundation viscosity attempted to decrease it. At some ranges of pipe length, the foundation viscosity effect seems to be more extreme. Increasing the fluid velocity leads to monotonic reduction in the system damping ratio. Two parameters, pipe length and fluid density which relate to the natural frequency of pipeline conveying fluid are studied in detail and the results indicate that the effect of Coriolis force on natural frequency is become more effective by increasing pipe length and fluid density besides increasing fluid flow velocity.