Increasing autonomy, efficiency and safety for Remotely Operated Vehicles (ROVs) is crucial for future subsea operations and requires accurate models for optimal control, operations and design. This involves precise modeling of the cable in conjunction with the ROV response. This paper presents a novel threedimensional cable model for Remotely Operated Vehicles using Euler-Bernoulli beam theory. The presented model is implemented in Matlab and takes into account the most important effects related to the response of underwater cables and ROVs. Following beam theory bending stiffness is also included, making the model applicable for low tension scenarios. The presented model is modified to allow for compression of the cable. The resulting non-linear equations are discretized spatially by the Galerkin finite element method and solved temporally by the Newmark-β time integration scheme. The model is verified experimentally in ocean tank experiments on a real ROV system. A numerical example is presented and the results are compared to previous published results. Lastly, a sensitivity analysis for the hydrodynamic parameters is presented.