The open-source code DualSPHysics is applied to simulate the interaction of sea waves with floating offshore structures, which are typically moored to the seabed, such as vessels, boats, floating breakwaters and wave energy converters (WECs). The goal is to develop a numerical tool that allows the study of the survivability of floating moored devices under highly energetic sea states, obtaining the optimum mooring layout to increase lifetime. The moorings are modelled by coupling DualSPHysics with MoorDyn, a lumped-mass mooring dynamics model. MoorDyn represents mooring line behaviour subject to axial elasticity, hydrodynamic forces in quiescent water, and vertical contact forces with the seabed. Calculated mooring tensions at the fairlead are added as external forces in order to compute the resulting response and motions of the floating structures in DualSPHysics. The coupled model has been validated against data from scale model tests generated during the experimental campaigns for the European MaRINET2 EsflOWC project. In order to evaluate the accuracy of the coupling implementation with the lumped-mass mooring model, free-surface elevation, motions of the floater and mooring tensions are numerically computed and compared to experimental data. Overall, the results demonstrate the accuracy of the coupling between DualSPHysics and MoorDyn to simulate the motion of a moored floating structure under the action of regular waves. Going forward, this modelling approach can be employed to simulate more complex floating structures such as floating wind turbines, buoys, WECs, offshore platforms, etc.