The problem of interaction between water wave and moored rectangular floating breakwater is studied using the semi-analytical Scaled Boundary Finite Element Method (SBFEM) in a two-dimensional vertical plane. The current study applies a generalized solution process by locating the scaling center within the bounded sub-domains instead of the body of structure, resulting in a homogeneous SBFEM equation. In spite of the merits of such choice for the scaling center that makes possible the analysis of non-rectangular objects, the method is changed to numerical-analytical one with its consequences. Such numerical solution in the problem of water wave radiation and diffraction is validated by comparing the results with previous reported studies. The generality and robustness of the current SBFEM-based model is also examined for non-rectangular cross-sections of the floating breakwater. Focusing on the proposed SBFEM-based model, the full wave-rigid body interaction is analyzed for a moored rectangular floating structure. Moreover, in order to make the linear numerical modeling accurate, taking into account the nonlinear aspects of the interaction problem, the artificial damping coefficients are quantified, and the relevant formula is derived.