Footbriges are often prone to vibrations induced by pedestrian loading. They are long and slender and their weight is moderate. One of the classical and famous examples is the transverse vibrations encountered on the millennium bridge in London. Horizontal vibration problems have received considerable attention due to millennium bridge vibration problem, but potential problems relating to vertical vibrations are more common. Vibrations from pedestrian loads are mostly limited to vibration frequencies below 5Hz. Most pedestrian bridges have several vibration modes below the above mentioned frequency. Increasing the stiffness could be a remedy to this vibration problem. And for a slender structure, increasing the stiffness often implies a corresponding increas in mass of the structure, whereby the desired effect is notachieved. Instead damping is often used to reduce the excessive vibration problem of footbridges by attaching additional dampers to the structre. London Millennium bridge was modelled inthis thesis in order to show the effect of tuned mass damper. There was a substantial reduction of the displacement of the bridge when tuned mass dampers were added to the bridge model.