This paper describes a coupled numerical model between a state-space model based on the Cummins’ equation and a lumped-mass mooring line solver for simulating moored floating structures. Viscous effects acting on the floating structure are taken into account using the quadratic term of the Morison equation. Additionally, wave induced loads acting on the mooring lines are also taken into account. The state space model has been validated using experimental data of a moored floating box in waves. The motions of the floating box in surge, heave and pitch; and the tension in the mooring lines were obtained in the numerical model and compared to the experimental data. The motions in terms of the Root Mean Square Error (RMSE) and the tensions in terms of the Relative Error (RE). Overall, the results show a good agreement between the numerical model and the experimental results with RMSE below 0.0013 m for the translational motions, 0.75 ° for the rotational motions and RE below 11.2 % difference for the mooring line peak tensions. Furthermore, the comparison of the state-space model and the experiments validated the estimated drag coefficients of the floating box. This modelling approach can be applied to more complex floating structures providing fast and reliable numerical simulations in weakly non-linear conditions for the design of marine renewable energy technologies.