This study addresses the critical challenge of liquid sloshing in marine engineering, particularly for prismatic tanks widely employed in modern liquefied natural gas (LNG) carriers. This study develops a modified Lagrangian meshless Smoothed Particle Hydrodynamics (SPH) framework to simulate two-dimensional sloshing dynamics in prismatic tanks. The numerical method incorporates pressure stabilization techniques, including density filtering and dynamic boundary particle treatment, to accurately resolve transient impact pressure characteristics. Simulations investigate sloshing behavior under different excitation frequencies, identifying significant pressure amplification at resonant frequencies compared to non-resonant conditions. Anti-sloshing measures involving vertical, T-shaped, and horizontal baffles were systematically evaluated. Results demonstrate that vertical baffles reduce wall pressure peaks by 87% through effective flow redirection, showing superior suppression performance. These findings provide practical references for baffle design optimization in LNG tank engineering applications. These findings provide practical references for the optimization of LNG ship compartment design and baffle arrangements in liquefied natural gas storage tank engineering applications.