Severe slugging in deepwater risers is a serious flow assurance problem that endangers the reliability of subsea production systems (pipelines, risers, and jumpers) by exposing them to fatigue loading, structural instability, and material damage due to its cyclic behaviour. Modelling this problem is very challenging because of its nonlinearity and the need to establish a coupled fluid–structure interaction (FSI) model that will reflect the physics of this problem. In this paper, a modified Plug Flow model and Euler–Bernoulli Beam theory are combined to establish the nonlinear FSI equation to investigate the relationship between the parameters of severe slugging and dynamic behaviour of deepwater riser structures. This FSI model is a higher-order partial differential equation of motion whose solution will describe the transverse vibration of the riser structure under severe slugging. To obtain the solution of this complex nonlinear equation of motion, a numerical method which based on a hybridized finite difference (FD) technique and a novel adaptive node-based height evaluator (ANHE) algorithm is programmed. The obtained solution is validated against a numerical FSI simulation in Abaqus. With the verified FSI model and the numerical solution technique (ANHE-FD), interactions between severe slugging parameters and dynamic response of deepwater risers are effectively investigated. The presented model and the numerical results obtained will improve in the fatigue and stability design of deepwater riser structures for offshore applications.