Three-dimensional motion equations of a marine Tethered Remotely Operated Vehicle (TROV) system with large elastic deformation and snap loads are formulated using the lumped parameter model. This formulation is simple and quite general in solving a wide range of offshore-related cable and pipeline problems using only three degrees of translational freedom for each computational nodes. The model is convenient in dealing with non-uniform features of the cable with low or even zero tension. The snap load that would damaged the sling is predicted by computing the dynamic tension and the instant configuration of the cable.This investigation may help avoid resonance, extend the cable life, reduce the test expense and avoid operating accidents.