Suspended steel cables are widely used in modern bridges today. However, as the spans of these bridges become larger, the length of the cables used increase consequently, so the problem of vibration in these cables becomes more evident. In some cases, it has been observed that the natural frequency of cables is consistent with the frequency of loads applied by natural forces, and the phenomenon of resonance has occurred in these bridges. These forces are caused by wind, rain, moving pedestrians, or vehicle on the bridge deck. The vibration of bridge cables can cause fatigue in the cable as well as at the junction of the bridge and the deck if it is not controlled by auxiliary dampers. Viscous dampers are among the devices that can be used to reduce the vibration of bridges. These dampers are used in several world-famous bridges today. However, due to the limited location of these dampers, which are usually possible up to 5% of the cable length from the end, the amount of damping applied to the cable by these dampers is limited and therefore it is very important to design suitable dampers in order to achieve maximum attenuation in the cable. These bridges include the Breton Bridge in France, the Sunshine Skyway Bridge in Florida, and the Aristotle Bridge in Japan. Nevertheless, the design of these dampers has been done experimentally using experiments such as wind tunnels. Therefore, it is necessary to be able to design methods for the design of these dampers without the expense of numerical analysis methods. This book examines such methods. The two numerical methods studied in this book. The first method is based on solving the equation governing cable dynamics by the series method. The second method is solving the equation of cable motion by the finite element method. Both methods are described in this book.