Lateral vibration equations of fluid-conveying pipes system are high order partial differential equations, and the analytic solution is difficult to obtain, so in this paper the numerical solution is obtained by the finite element method. Firstly, the finite element equations of lateral vibration of fluid-conveying pipes were set up, and four kinds of boundary constraints were proposed. The modal analysis of vibration system was carried out by using mode decomposition method, and the system responses were solved by using Newmark method. The impact of pipe span, flow rate, fluid pressure, flow rate disturbance and fluid pressure disturbance on the modes and responses of vibration system were studied. The research results provided theoretical support for the vibration reduction research of fluid-conveying pipes.