Damped oscillation of Newtonian liquid in a vertical U-tube is one of the well known phenomena and the solutionof this liquid motion for the laminar flow regime in the circular pipe was solved,however,generally speaking,even if the period of the oscillational motion by this solution is nearly coincided with that of the experimental re-sult,the estimation of the damped oscillational process with lapse of time by the solved equation is not in agree-ment with that of the experimental result.Therefore basing upon the experimental results of the velocity distribu-tions of the oscillational motion in the circular U-tube for the Newtonian and non-Newtonian liquids,the velocitydistribution of the Bingham plastic flow is assumed.The solutions of the damped oscillation and also of the ver-tical falling and rising velocities of the free surface in the vertical U-tube of the diameters D=10mm,20mm and40mm are compared with water and water-glycerine solution for the Newtonian liquids and the acrylicco-polymer solutions for the non-Newtonian liquid.The comparisons of these solved equations by the new flowmodel are shown in good agreement with the experimental results.The above stated results are described indetail. Damped oscillation of Newtonian liquid in a vertical U-tube is one of the well known phenomena and the solution of this liquid motion for the laminar flow regime in the circular pipe was solved, however, generally speaking, even if the period of the oscillational motion by this solution is nearly coincided with that of the experimental re-sult, the estimation of the damped oscillational process with lapse of time by the solved equation is not in agree-ment with that of the experimental result. Before basing upon the experimental results of the velocity distribu-tions of the oscillational motion in the circular U-tube for the Newtonian and non-Newtonian liquids, the velocity distribution of the Bingham plastic flow is assumed. the solutions of the damped oscillation and also of the ver-tical falling and rising velocities of the free surface in the vertical U-tube of the diameters D = 10mm, 20mm and 40mm are compared with water and water-glycerine solution for the Newtonian liquids and the acrylic co-polymer solutions for the non-Newtonian liquid. The comparisons of these solved equations by the new flow model. are shown in good agreement with the experimental results. The above description results are described indetail.