In re-entry,the drilling riser hanging to the holding vessel takes on a free hanging state,waiting to be moved from the initial random position to the wellhead.For the re-entry,dynamics calculation is often done to predict the riser motion or evaluate the structural safety.A dynamics calculation method based on Flexible Segment Model (FSM) is proposed for free hanging marine risers.In FSM,a riser is discretized into a series of flexible segments.For each flexible segment,its deflection feature and external forces are analyzed independently.For the whole riser,the nonlinear governing equations are listed according to the moment equilibrium at nodes.For the solution of the nonlinear equations,a linearization iteration scheme is provided in the paper.Owing to its flexibility,each segment can match a long part of the riser body,which enables that good results can be obtained even with a small number of segments.Moreover,the linearization iteration scheme can avoid widely used Newton-Rapson iteration scheme in which the calculation stability is influenced by the initial points.The FSM-based dynamics calculation is timesaving and stable,so suitable for the shape prediction or real-time control of free hanging marine risers.