The scaled boundary finite element method (SBFEM) is introduced for the investigation of the liquid sloshing in an annular cylindrical container with the coaxial porous structures. The main advantages of the SBFEM for this problem is that only the outer wall of the annular tank is discretized while the inner wall and the porous structures need not be treated, which is not only convenient for the generation of mesh, but also reduces the spatial dimension by one. Meanwhile, the solutions of the velocity potential are analytical in the radical direction of the scaled boundary coordinate system. In this paper, two types of the porous structures, that are, the circular and the arc-shaped porous structures, are taken into account. For the arc-shaped system, a virtual circular by extending the arc-shaped structure porous is introduced and one can set the porous-effect parameter of the virtual section to infinity, so that the whole flow domain can be divided into two sub-domains by the porous structure as the same approach with the circular system. By the assumption of the incompressible, inviscid, and irrotational flow and using the variational principle, the SBFEM governing equations with respect to the radical coordinate of the velocity potential in each sub-domain are obtained. Then, the governing equations can be solved analytically by introducing the Bessel functions and the modified Bessel functions as the base solutions. The excellent efficiency and accuracy of the proposed formulations are demonstrated by comparing the SBFEM numerical results with the analytical solutions. In addition, the effects of the different parameters for sloshing characteristics, such as the porous-effect parameter, radius of porous structure, standing wave number, opening degree and location of the arc-shaped porous structure are further studied.