<p>Flow-induced vibrations of pipes conveying slug flow are frequently encountered in nuclear engineering, aerospace, and chemical industries. Compared with pipes conveying single-phase fluids, slug flow is more likely to induce parametric resonance in pipe systems. In this study, slug flow is modeled as a liquid piston with sinusoidally varying density, where the slug frequency changes with both position and time. A dynamic model for a cantilevered L-shaped pipe conveying slug flow is established based on the absolute nodal coordinate formulation (ANCF). The static deformation results obtained from the model are validated against the finite element method (FEM), confirming the reliability of the proposed model. The results indicate that the amplitude of fluid density fluctuation, fluctuation frequency, and flow velocity significantly affect the nonlinear vibration responses of the pipe. When fluid density fluctuation is neglected, the pipe exhibits only static deformations as the flow velocity increases. For large fluctuation amplitudes, the pipe can exhibit quasi-periodic and chaotic responses. At subcritical flow velocities, pipe instability primarily manifests as a periodic response. Moreover, the pipe can experience larger vibration amplitudes in the low-frequency range. This study provides a theoretical basis for predicting flow-induced vibrations in complex piping systems conveying slug flow in engineering applications.</p>