The vibration of damped pipeline conveying fluid with the effect of fluid-structure interaction is known to pose challenging problems in oil and gas industry. In this study, the natural frequency of fluid-structure interaction in pipeline conveying fluid set on viscoelastic foundation is investigated by using finite element method. The governing partial differential equation is modelled based on Euler-Bernoulli beam theory. By applying Galerkin weighted residual method, the stiffness, damping, and mass matrices are obtained. For a given boundary condition which is simply supported, two components of the foundation (foundation stiffness and damping) which are influencing the damped natural frequency of the pipeline are studied for different fluid velocity. The results indicate that increasing the foundation stiffness from 10 kN/m3 to 30 kN/m3 increases the natural frequency of the pipeline, while increasing the foundation damping from 1 kN.s/m3 to 3 kN.s/m3 and fluid velocity decrease the natural frequency of the pipeline. The accuracy of the results obtained is validated against data from literature. © The Authors, published by EDP Sciences, 2017.