The internal flow in gas-liquid mixing riser often displays a flow pattern known as slug flow, in which gas and liquid are alternately distributed. Dynamic effects due to slug flow is normally most obvious in areas along the riser with high curvature, which is caused by the centrifugal load component. The global riser response to this excitation can be predicted by nonlinear time domain analysis using the load model as described for slug flow conditions. In this study, the riser with internal slug flow is modeled under the framework of Arbitrary-Lagrange-Euler (ALE) description by using the Absolute Node Coordinate Formula (ANCF). The riser is discretized into ANCF cable element based on the Euler-Bernoulli beam assumption, while one-dimensional moving medium modeling method with time-varying density is used to model slug element. Compared with other FEA models of riser subjected to internal flow, the ALE-ANCF model allow easily modeling of complex mass flow and has the advantages of high speed and high precision in handling large deformation of riser, especially for the compliant riser configurations. Numerical simulations of two simplified models are carried out to validate the developed model, then the dynamic response such as displacement, tension force and bending moment of the riser conveying slug flow are analyzed.