Several models of a non-linear rail three-piece bogie container wagon have been developed by using GENSYS software to study the effects of the initial excitation conditions to the determination of rail wagon’s critical hunting speed and the trajectories and characteristics of the wheelset lateral movement during wagon hunting. The effect of uneven loading distribution on a container wagon to the wagon lateral instability is also investigated. Based on the simulation results, the wagon hunting is the type of bogie hunting, and the hunting behaviours are dependent on the initial excitation conditions and wagon speed. The initial excitation condition based on a certain initial lateral track irregularity can generate the full bogie hunting compared to the initial carbody’s lateral and yaw velocities that are the default widely used in the GENSYS setting. The two bogie lateral movement trajectories can have a phase of about 900 or be in-phase dependent on the wagon speed. The heavy loading on a bogie can improve the bogie hunting, and the uneven loading can change the hunting pattern.