This thesis discusses a new mechanical network element, Inerter, from the analogy of mechanical and electrical networks. Firstly we probe into the concept and principle of Inerter and make two kinds of Inerter models. Secondly we combine Inerter with traditional suspension element, i.e spring and damper, and discuss the transfer functions of the networks. Thirdly a complete plateform is constructed to verify the network properties experimentally. Finally we consider a simple building suspension model to show the benefits of applying Inerter to building suspension design. Using an Inerter to simulate a heavy mass, we are able to assemble a building model to experimentally verify the suspension design. The Inerter properties are used to decrease the vibrations on specific frequency range to building.