Track irregularity is the main excitation source of the vehicle-track coupling system vibration. Track irregularities can be divided into track profile irregularity, track cross-level irregularity, track alignment irregularity, and track gauge irregularity. In vehicle-track coupling dynamics, track random irregularities are typically characterized using power spectral density (PSD) functions, which play a crucial role in vibration analysis. This chapter provides an overview of the PSD functions adopted by various countries, including the United States, Germany, China, and Japan, for describing track irregularities. Additionally, it introduces a numerical method for generating track random irregularity samples based on these track irregularity PSD functions.