Placing porous media in a water tank can change the dynamic characteristics of the sloshing fluid. Its extra damping effect can mitigate sloshing and, thereby, protect the integrity of a liquefied natural gas tank. In addition, the out-of-phase sloshing force enables the water tank to serve as a dynamic vibration absorber for floating structures in the ocean environment. The influence of porous media on wave-induced sloshing fluid in a floating tank and the associated interaction with the substructure in the ambient wave field are the focus of this study. The numerical coupling algorithm includes the potential-based Eulerian–Lagrangian method for fluid simulation and the Newmark time-integration method for rigid-body dynamics. An equivalent mechanical model for the sloshing fluid in a rectangular tank subject to pitch motion is proposed and validated. In this approach, the degrees of freedom modeling of the sloshing fluid can be reduced so the numerical computation is fast and inexpensive. The results of the linear mechanical model and the nonlinear Eulerian–Lagrangian method are correlated. The dynamic interaction between the sloshing fluid and floating body is characterized. The effectiveness of the added porous media in controlling the vibration and mitigating the sloshing response is confirmed through frequency response analysis.