In the process of underwater cable motion modeling，there will be low stress relaxation，large bending or torsion and other deformations. Therefore，it is necessary to finely divide the spatial discrete micro-elements and the time domain solution step size to describe the cable curvature change and avoid numerical solution singularity. This processing method makes the solution of underwater cable motion response extremely inefficient，and may even cause calculation errors caused by the accumulation of truncation errors and rounding errors in the process of numerical integration，which makes it impossible to describe the real state of underwater mooring，towing and other systems. In order to accurately describe the bending，torsion and other deformation states of the underwater flexible cable and its influence on the mathematical model of the motion system，the cubic spline interpolation method is used to construct the micro-element space form of the underwater cable，and the continuous underwater cable is processed by nonlinear discrete processing. The motion equation of the cable micro-element in the domain is solved by the Galerkin margin elimination method，and the mathematical model and solution method of the dynamic motion of the underwater cable including the bending moment and torque are established. The accuracy of the model is verified by comparison with theoretical numerical calculation data and offshore experimental data，which can provide an efficient design method for the engineering application of underwater mooring，underwater towing and other systems.
