Most of the structural engineering designs such as trusses and frames, aircraft and aerospace structures, bridges, machine members and many other applications are built up by connecting structural components through mechanical connections or joints. Under the dynamic loads, such assembled designs need sufficient damping to limit excessive vibrations otherwise those uncontrolled vibration can lead to catastrophic situations. The damping mechanism of various jointed structures can be explained by considering the energy loss due to friction and the dynamic slip produced at the interfaces and mainly starts from two sources. One is the internal or material damping which is innately low and the other one is the structural damping due to joints. It is estimated that structures consisting of bolted or riveted members contribute about 90% and rest by others of the damping through the joints. So we need to study the damping characteristics of the mechanical joints. This book gives the brief on theory and analysis of structural joints considering free vibration.