In mixed traffic scenarios, a certain number of pedestrians might coexist in a small area while interacting with vehicles. In this situation, every pedestrian must simultaneously react to the surrounding pedestrians and vehicles. Analytical modeling of such collective pedestrian motion can benefit intelligent transportation practices like shared space design and urban autonomous driving. This work proposed the sub-goal social force model (SG-SFM) to describe the collective pedestrian motion under vehicle influence. The proposed model introduced a new design of vehicle influence on pedestrian motion, which was smoothly combined with the influence of surrounding pedestrians using the sub-goal concept. This model aims to describe generalized pedestrian motion, i.e., it is applicable to various vehicle-pedestrian interaction patterns. The generalization was verified by both quantitative and qualitative evaluation. The quantitative evaluation was conducted to reproduce pedestrian motion in three different datasets, HBS, CITR, and DUT. It also compared two different ways of calibrating the model parameters. The qualitative evaluation examined the simulation of collective pedestrian motion in a series of fundamental vehicle-pedestrian interaction scenarios. The above evaluation results demonstrated the effectiveness of the proposed model.