The article presents the results of a study of vibration process in pipelines conveying fluid or gas. A mathematical model pipeline was used in the form of cylindrical shell and a viscoelastic foundation in the form of two-parameter model of the Pasternak. The hereditary Boltzmann-Volterra theory of viscoelasticity is used to describe viscoelastic properties. The effects of the parameters of the Pasternak foundations, the singularity in the heredity kernels and geometric parameters of the pipeline on vibrations of structures with viscoelastic properties are numerically investigated. It is found that an account of viscoelastic properties of the pipeline material leads to a decrease in the amplitude and frequency of vibrations by 20–40 %. It is shown that an account of viscoelastic properties of soil foundations leads to a damping of vibration process in pipeline.