The paper discusses the model of transverse vibrations of a pipe induced by flow velocity pulsation. The motion is described by a system of two non-linear partial differential equations with periodically variable coefficients. The analysis uses the Galerkin method with orthogonal polynomials as the shape functions. The instability regions are determined by Floquet's method. The influence of selected parameters on natural frequencies and on the character and level of vibrations is studied. The possibility of the excitation of periodic and quasi-periodic oscillations is demonstrated. The results of theoretical analysis are compared with the experimental data.