Tuned Liquid Dampers (TLD) are used to limit horizontal vibrations in structures, and offer practical alternatives to Tuned Mass Dampers (TMD). However, to our knowledge, liquid damping systems have not been developed to reduce vertical vibrations. In this work, we develop a model for a Vertical Motion Liquid Damper (VMLD), idealized as a discrete, two degree of freedom system. One degree of freedom represents the 'target' structure that is to be damped, and the other represents the approximate, one-dimensional motion of a liquid in a U-shaped tube. Internal losses due to the fluid oscillation serve to limit and control motions of the target structure. The U-shaped tube has a flexible joint such that one vertical portion and the horizontal portion of the tube remain fixed, and the remaining vertical portion of the tube is affixed to the vibrating structure, allowing the liquid to become excited. The equations of motion are derived using Lagrange's Equations, and are integrated using Runge-Kutta algorithms that are available in Matlab. An experimental model was built in the laboratory, consisting of a mass attached to the end of a cantilevered beam (corresponding to the target structure), and a U-tube made from PVC pipe. The various damping and stiffness parameters of the system were calibrated independently based on experimental data. Measured data from the experimental model show reasonable agreement with numerical simulations.