<p>The sloshing control by lateral porous baffles in a swaying and rolling rectangular tank has been investigated using analytical and numerical approaches. First, the potential-based MEEM (matched eigenfunction expansion method) solutions were expressed by the series of vertical eigenfunctions and determined by solving algebraic equations derived from matching conditions at adjacent boundaries. Particularly, the vertical eigenfunctions in the lateral porous baffle-presence region were completed by solving the nonlinear dispersion equation by applying Darcy’s law at the porous baffle. Second, a dual boundary element method (DBEM) using the linear Darcy’s and nonlinear quadratic velocity models at the porous baffle was also independently developed for cross-verification and more generalized baffle geometry. After confirming the good agreement between both solutions and experiments, we investigated the effect of the lateral baffle’s porosity, length, inclined angle, and submergence depth on the sloshing suppression. It is noted that the lateral porous baffles attached to the tank wall significantly contributed to suppressing violent sloshing behavior. Also, the quadratic velocity model showed a closer agreement with experimental results than linear Darcy’s model in high-frequency regions where nonlinearity dominates.</p>