A porous-media-tuned liquid damper (PMTLD) can serve as an effective and economical dynamic vibration absorber. Placing porous media within a water tank can improve the capacity for energy dissipation and optimize the performance by varying its material properties. Two numerical models are adopted to simulate the sloshing problem in PMTLD and the dynamics of a floating platform in waves. Besides, the effectiveness of response mitigation can be verified numerically. The first potential-based approach employs a mixed-type boundary value problem (BVP) solver and a free-surface particle tracker. This approach not only simulates the inviscid water wave but also includes the nonlinear damping of the PMTLD via a quadratic Forchheimer term. Another equivalent mechanical model is used to reduce the degree-of-freedom of the PMTLD system. The Newmark method is incorporated to solve the rigid-body dynamics. The second viscous approach uses the finite element method (FEM) to spatially discretize the Navier–Stokes (NS) equations and handles the free surface via the volume of fluid (VOF) and the level set (LS) equations. The multiphase simulation is implemented by computational modeling toolkits, Proteus and Chrono, for the fluid and solid phases, respectively. The correlations between potential flow and two-phase NS models are presented. The PMTLD is designed by analogy with the tuned mass damper (TMD). Numerical results show that the PMTLD can effectively reduce the structure's dynamic response in terms of vibration amplitude around resonance. Such damping devices have great potential for offshore platforms and wind turbine design.