Simplification of a complex model is an analytical method commonly adopted in engineering design and academic research. A simplified theoretical analysis model can help project planners or researchers to develop an integrative view of the effect of each component on the system performances, which allows them to understand the related engineering phenomena and make proper engineering judgments. Based on the widely used Maxwell constitutive model for anti-yaw dampers, a simple 4 degree-of-freedom model is established to derive a set of analytical formulas, including those for critical speed, anti-yaw damper force transfer function, and rational resistance factor, which control the stability, ride quality, and curving performance of rail vehicles, respectively. Based on the proposed analytical formulas, the impact of damper parameters and mounting positions of the anti-yaw damper on the stability, ride quality and curving performance are analyzed. Finally, trade-offs among stability, ride quality, and curving performance are also discussed.