This paper analyzes the coupled nonlinear tangential-normal waves that propagate along underwater cable suspensions. Taken with the recently developed linear theory governing the in-plane structural waves (Behbahani-Nejad and Perkins, 1996) and an analysis of nonlinear out-of-plane waves for submerged cables (Behbahani-Nejad and Perkins, 1997), this investigation contributes further understanding toward a nonlinear three-dimensional theory for wave propagation along fluid-loaded cables. The nonlinearities present in the in-plane model render the cable/fluid model intractable by exact analytical methods. A numerical solution is pursued in this study using finite difference algorithms. To this end, an infinite cable domain is divided to two subdomains, namely an interior (finite computational) domain and exterior (infinite far-field) domain. Closed-form solutions for the approximate linear theory are employed for the far field in constructing nonreflecting boundary conditions for the computational domain. Numerical results highlight the governing role of nonlinear hydrodynamic drag for underwater cable suspensions. The numerical results further demonstrate that most analyses of cables in air are not useful for underwater cable applications.