The subject of this research is to model the probability of accepting package delivery tasks in Crowd-Shipping (CS) systems focusing on shipping packages by Public Transportation (PT) passengers. Real-world implementation of such a PT-based CS initiative requires a proper grasp of the behavior of crowd shippers, package receivers, and senders, among which crowdshippers are at the center of attention. Given survey data collected from 2,208PT passengers in the Sydney metropolitan area, this study constructs a model for package delivery task acceptance among PT passengers who express a willingness to participate as crowdshippers. A Latent Class (LC) choice model is developed and estimated to explore different classes of participant characteristics and preferences for accepting CS delivery tasks, under different levels of offered incentive, package weight, and required detour distance at the destination. As a key finding, the model identifies three classes, namely “leisurely”, “avid”, and “skeptical” users with class sizes of 19%, 53%, and 28%, respectively. Leisurely users tend to be majorly employed with relatively higher ages and lower PT trip frequency per month. This class shows a potential desire to take CS tasks as long as they are not logistically burdensome. Avid users, forming the largest class of the population, are mostly younger PT passengers who are less sensitive to task difficulty and might accept even CS tasks with minimum incentives (around AU$3). Skeptical users, displaying high PT trip frequency per month and high income, are unwilling to accept the CS tasks unless get compensated well.