<p>This study investigates the shimmy phenomenon in rail vehicles equipped with pneumatic rubber-tired running gear—an area with limited prior research. A dynamic model of an Automated People Mover bogie was first developed, revealing through numerical simulation that shimmy manifests as a self-excited vibration involving coupled yaw and roll motions. An analytical expression for the resulting limit cycle was subsequently derived, showing good agreement with numerical results by incorporating gyroscopic coupling effects. Based on this analytical representation, the effect of key dynamic parameters on the nonlinear vibration characteristics was examined. The analysis indicates that increasing the yaw damping of the guiding frame is the most effective approach for suppressing shimmy. Additionally, the amplitude–frequency response under forced excitation was explored, demonstrating resonance induced by synchronization near the natural yaw frequency. Overall, this study combines analytical and numerical methods to offer theoretical insight and a methodological foundation for understanding shimmy behavior in pneumatic rubber-tired rail vehicles.</p>