In development of high speed Rigid conductor line(R-bar) over 250km/h, it is important to develop the method to anticipate the mechanical stability of the R-bar and of the transition structure which connects the flexible Overhead Contact Line. To do this, firstly, the FE(Finite Element) model for a transition structure was established and the initial deformed configurations due to gravitational force is obtained by a static analysis and the pantograph was modeled by a simplified mass-spring-damper system and the contact behavior between conductor and pantograph was defined by the penality method. Secondly, FE analysis results were reviewed with the test results of contact force between conductor and pantograph at the low speed of train. Finally, using the established analysis method, the evolution of contact forces was performed for a newly designed high speed R-bar and for its transition structure.