In this paper, a cantilevered pipe model which conveys a two-phase, solid-liquid flow is numerically studied. First, the dynamic equation of cantilever pipeline is established based on an energy method and Hamiltonian variational principle. Then, the above partial differential equation is discretized by the Galerkin method of finite order to obtain a system of ordinary differential equations. Finally, the eigenvalue method and Newton-Raphson method are applied to study the stability characteristics of the cantilever pipeline model. The dimensionless aspect ratio, the dimensionless gravity coefficient, and the dimensionless solid-phase volume under four different dimensionless ended mass are selected to analyze the impact on the critical velocity. The results show that when the inner flow velocity is less than the critical velocity, all of the imaginary parts of the characteristic frequencies of the system have positive values, and the vibration form of the structure is damped. However, as the inner flow velocity exceeds the critical velocity, the imaginary part of a certain characteristic frequency of the system will appear to be negative, and resulting in the structure vibration form displaying the flutter instability. In addition, the influence of the end lumped mass on the critical velocity decreases with the increase of the gravity coefficient. When the gravity coefficient increases to a certain value, the critical velocity value is slightly affected by the end lumped mass. When the aspect ratios and the solid phase ratio are small, the critical velocity decreases with the increase of the mass at the end. When the aspect ratios and the solid phase ratio are larger, the critical velocity no longer shows a monotonous change trend, but a more complex change trend. The research has important theoretical and engineering value for the reasonable design of cantilever pipeline in the early stage and the safety work during the service period.