In this study, a finite element analysis was used to analyze the stress state and vibration characteristics generated by continuous contact between wheels and rails when driving urban railway vehicles. The rails applied to the analysis were divided into straight and curved shapes, and three-dimensional modeling was performed to analyze the changes in structural characteristics of wheels and rails when driving on straight and curved rails. As a result of the analysis, the stress characteristics were up to 6.5 MPa on a straight rail and 9.81 MPa on a curved rail, and it is believed that this increase in stress will increase noise due to an increase in friction at the interface. The vibration characteristics of the wheels and rails showed similar behavior from the 3rd mode to the 9th mode of the rail to the intrinsic vibration characteristics from the 4th mode to the 6th mode of the wheel.