Fish cages composed of ropes and nets will suffer more severe marine environmental conditions in deep sea. In order to measure the maximum tension and normal displacement of the ropes corresponding to the net panel, a finite element method was proposed to evaluate the tension response of ropes by coupling the Morison models and Screen models to calculate the hydrodynamic forces on ropes and nets separately. The tension response of the ropes in two independent nets A and B at different water depths was studied under the pure current and wave-current interaction conditions. For pure current conditions, statistical analysis of the numerical results shows that the average maximum tension and normal displacement of the ropes are growing as the current grows. The average maximum tension and normal displacement of the ropes in net A were significantly larger than those in net B under the wave-current interaction conditions. The average maximum tension and normal displacement of the ropes decrease with the increase of the design wave period in net A, while the average maximum tension of network B increases gradually. This study will be useful for the research on the coupling of ropes and nets.