Increase of track maintenance costs and change of track geometry are due to the vibration of ballasted railway. The aim of this thesis work is to model train-track system as a multiply degree of freedom systems by Lump Parameter Method. In this model, there are two system which both are modeling as series of mass, dampers and stiffness with the irregularity of rail as exciting signal. The two subsystems are coupled by Nonlinear Hertz contact theory, and then the dynamic system is simulated in Matlab by Newmark Beta method and Runge-Kutta method to obtain the dynamic situation of the system. In addition, the ballast parameters are described in details, and the rail is treated as Euler beam. Moreover, estimate the impact of the other factors as rail, ballast, sleeper, the vehicle speed and the irregularity level of vibration system. The model is validated by comparing with the experiment result done by predecessor. Fundamental fracture analysis of track is also completed, discussed in static analysis, as a start of further work such as dynamical one.