Abstract: For small-amplitude liquid sloshing, the viscous dampingnear the free surface is an important part of the whole damping in partlyfilled liquid container. The damping is affected by many factors and isdifficult to calculate with a reasonable accuracy. In order to compute thedamping in partly filled rigid circular cylinder more reliably, a volume offluid method based on finite volume method is used. It is difficult tocompute damping precisely through numerical computation based on Stokesequations, in which the adhesion wall boundary condition can not besimultaneously satisfied at both the bottom wall and side wall. The dampingcomputation discrepancy of this method based on Stokes equations depends onthe liquid height ratio, h/R, where h is the liquid height and R is the radiusof the cylindrical container. The present method maintains all the wallboundary conditions, both side wall and bottom wall, with no slip conditionsand can give an exact damping value instead of an estimation range. Thesimulation damping results show a better agreement with the publishedexperimental data, especially for liquid height ratio h/R < 1.