Abstract: This paper is concerned with the calculation of damping and natural frequencies of sloshing liquid with small amplitude in fixed containers. An eigenvalue equation is presented and converted to a non-symmetric general eigenvalue problem. Boundary layer damping based on the Stokes theory is also integrated into the equivalent damping. Two examples are given and compared with the theoretic and experimental data. The present new algorithm can be used to calculate the damping and natural frequencies of small amplitude sloshing for containers with arbitrary geometry shape.