The natural frequency of surface wave, which has been derived from a vertically oscillating circular cylindrical vessel in inviscid fluid, was modified by considering the influence of surface tension and weak viscosity. Many flow patterns were found at different forced frequencies by numerical computation. In addition, the nonlinear amplitude equation derived in inviscid fluid was modified by adding viscous damping and the unstable regions were determined by stability analysis. The natural frequency of surface wave, which has been derived from a vertically oscillating circular cylindrical vessel in inviscid fluid, was modified by considering the influence of surface tension and weak viscosity. Many flow patterns were found at different forced frequencies by numerical computation. , the nonlinear amplitude equation derived in inviscid fluid was modified by adding viscous damping and the unstable regions were determined by stability analysis.