Floating structures for single offshore renewable energy devices, i.e. wave energy converters, tend to be significantly smaller than those of the traditional offshore industry and the interaction between floater motions and mooring line dynamics become important. Installation sites are generally subject to powerful waves and currents experiencing more dynamically excited motions. Water depths are also lower, ranging generally from 50 m to 200 m and mooring systems are to be designed to assure the station keeping of them while not interfering with the power conversion. However, floater motions may induce large dynamic tensions on mooring lines, making quasistatic analyses inaccurate in terms of design tension while non-linear time domain simulations too time consuming. This paper introduces a numerical model of lumped mass for mooring lines and rigid body motions for the floating structure coupled by means of kinematic relations, and its subsequent linearization, which is solved in the frequency domain. The linearized model is applied to a two-body floating spar type oscillating water column, subject to the 36 most occurrent sea states at the BIMEP site. Its accuracy is verified through a comparison with the equivalent time domain simulation and a review of the results and its limitations are also pointed out.