The derivation of a discrete mooring model for floating structures is presented in this paper. The method predicts the steady-state solution for the shape of an elastic cable and the tension forces under consideration of static loads. It is based on a discretization of the cable in mass points connected with straight but elastic bars. The successive approximation is applied to the resulting system of equations which leads to a significant reduction of the matrix size in comparison to the matrix of a Newton–Raphson method. The mooring model is implemented in the open-source computational fluid dynamics (CFD) model REEF3D. The solver has been used to study various problems in the field of wave hydrodynamics and fluid–structure interaction. It includes floating structures through a level set function and captures its motion using Newton and Euler equations in six degrees-of-freedom (6DOF). The fluid–structure interaction is solved explicitly using an immersed boundary method based on the ghost cell method. The applications show the accuracy of the solver and the effects of mooring on the motion of floating structures.