Vehicles moving in a non-lane-disciplined traffic stream frequently look for the opportunities to overtake/pass the leading vehicle(s) without compromising the safety. The lateral movement would be more frequent when a vehicle follows a slow vehicle and look for overtaking opportunity. The magnitudes of the lateral shift would be different for different vehicle classes depending on the size and the maneuverability of the vehicle. The present study aims to quantify the lateral positioning characteristics of different vehicle classes and their distribution. From the traffic videos collected from Hyderabad city, India, the trajectories of each vehicle have been extracted using an image processing software TRAZER. The extracted trajectories were corrected for any random noise using CEEMDAN algorithm. The lateral position information of each vehicle was extracted for every 0.04 sec from the trajectory data, and the cumulative lateral shifts during a longitudinal unit movement were calculated. The analysis shows that the lateral shifting characteristics are different for different vehicles classes. A maximum lateral shift was observed in the cases of the Motorized two-wheeler (MTW) compared to the other vehicle classes. Further, the probability distribution of lateral shifts of different vehicles classes was investigated. It was found that, except for MTW, the lognormal distribution could model the lateral shifts characteristics of different types of vehicles. The lateral shift characteristic of the MTW could be modeled as a Weibull process. The findings of the study would enable better modeling of the lateral dynamics of different vehicle classes in a non-lane-disciplined traffic stream. © 2020 The Authors. Published by Elsevier B.V.