This thesis discusses the concepts of a newly-developed mechanical network element, called Inerter. We apply this idea to train suspension systems by combining Inerter with the traditional suspension systems, and compare the performance benefits in lateral stability of the train. We build the train suspension model on a multi-body-system-builder, AutoSim, and verify it by an existing train model with twelve degree-of-freedom(DOF). Furthermore, the model is extended to sixteen DOF to explore the performance limitation by inerters. From the simulation results, inerters are shown effective in improving the lateral stability of the train.