The liquid sloshing resonance may cause the structural instability even damage of vessel walls. The porous baffles have the ability to dissipate the energy of sloshing motion and suppress the sloshing force on the container walls. The liquid is assumed to be incompressible and inviscid, oscillations amplitudes of liquid are treated to be small, and the walls of tank are chosen as rigid. The fluid domain should be divided into several regions by the porous baffles and the virtual boundaries. The fluxes across those porous baffles satisfy continuity, and the difference of pressure between each baffle's sides is linearly proportional to the flow velocity through the baffles. The porous baffles are fixed at the container in this paper, and the external excitation acting on the porous baffles with flow velocity form also should be added to the boundary conditions. Meanwhile, the normal velocity and pressure of virtual boundary named matching boundary between each region sides should remain continuous. The boundary element method (BEM) with Green's theorem based on the potential flow is conducted with the governing equation and the corresponding to the boundaries of each region. The final entire equation of liquid motion is formulated by assembling the equation of each region. The numerical model is validated by comparing the results with those of the available literatures, good agreement is achieved. The results are proposed for the two dimensional rectangular tank with the top or bottom-mounted vertical porous baffles, multiple mounted two-sided porous baffles, middle-mounted circle porous baffle, top or bottom-mounted semicircle porous baffles, top or bottom-mounted T-shaped porous baffle, and center-mounted cosine-shaped porous baffle. The effects of the porous baffle length, porosity and design on the sloshing force, wave surface elevation, and velocity field are studied and some conclusions are obtained.