The development of railway vehicles involves the proper selection of design parameters not only to achieve high speed but also to reduce the vibration of the train. In this study an analytical model of a freight car is developed to find the critical speed. The freight car can generate the snake motion of the lateral and yawing motion of the car body, the bogie, and the wheelset. Numerical analysis for the nonlinear equation motions with 17 degrees of freedom showed the running stability and critical speed due to the snake motion. Also, the vibration modes of the freight car was calculated using ADAMS/RAIL, which showed that the critical speed have the yawing modes of the car body and the bogie. Finally this paper shows that the snake motion of the vehicle can be controlled with the modifications of the design parameters.