Liquid sloshing is a kind of very complicated free surface flow and exists widely in many fields.In order to calculate liquid sloshing damping precisely a volume of fluid method based on finite volume scheme is used to simulate free surface flows in partly filled cylindrical containers.A numerical method is pre-sented to simulate the movement of the free surface flow,in which a piecewise linear interface con-struction scheme and an unsplit Lagrangian advection scheme instead of Eulerian advection scheme are used.The damping performance of liquid sloshing in cylindrical containers under fundamental sloshing mode is investigated.There are four factors determining the surface-wave damping:free surface,boundary-layer,interior fluid and contact line.In order to study different contributions from these four factors to whole damping,several examples are simulated.No-slip and slip wall boundary conditions on both side wall and bottom wall of the cylindrical containers are studied to compare with the published results obtained by solving Stokes equations.In the present method the first three main factors can be considered.The simulation results show that the boundary-layer damping contribution increases while the interior fluid damping contribution decreases with increase of Reynolds number. Liquid sloshing is a kind of very complicated free surface flow and has widely in many fields. In order to calculate liquid sloshing damping precisely a volume of fluid method based on finite volume scheme is used to simulate free surface flows in partly filled cylindrical containers. A numerical method is pre-sented to simulate the movement of the free surface flow, in which a piecewise linear interface con-construction scheme and an unsplit Lagrangian advection scheme instead of Eulerian advection scheme are used. The damping performance of liquid sloshing in cylindrical containers under fundamental sloshing mode is investigated. Here are four factors determining the surface-wave damping: free surface, boundary-layer, interior fluid and contact line. In order to study different contributions from these four factors to whole damping, several examples are simulated. No -slip and slip wall boundary conditions on both side wall and bottom wall of the cylindrical containers are studied to compare wi th the published results obtained by solving Stokes equations.In the present method the first three main factors can be considered. the simulation results show the the boundary-layer damping contribution increases while the interior fluid damping contribution increases with the increase of Reynolds number.