Vortex-induced vibration (VIV) of the riser considering both external flow and multiphase internal flow is a complex fluid-structure interaction problem. Due to its flexible feature, steel catenary riser (SCR) may be more affected by internal flow than top-tensioned riser (TTR). Firstly, the semi-empirical time domain VIV model of riser with internal flow is introduced, and the theories of gas-liquid flow and solid-liquid flow are applied to modify the model. Then the VIV of TTR and SCR with internal flow are compared. Subsequently, the VIV of SCR with gas-liquid flow and solid-liquid flow are calculated, and their different effects are discussed. The results show that internal flow triggers higher-order modes of VIV and enlarges the fatigue damage in general. With similar length, internal flow has more significant impact on SCR than TTR. The increase of liquid volumetric flow rate, solid production and gas volumetric quality enlarges the modal order and fatigue damage. The increase of solid volumetric quality and solid density reduces the modal order and fatigue damage. Compared with gas-liquid flow, solid-liquid flow may decrease the VIV amplitude and reduce the fatigue damage.