Earlier work by the author developed a two-dimensional car-following model by taking into account the lateral discomfort experienced between the neighbouring vehicles moving in the same direction. This incorporation of lateral friction in car-following theory may offer a potential breakthrough in the field of microscopic simulation. However, that model was based on a small-scale scrutiny in which the interactions between only two or three vehicles were analysed in isolation. The treatment of the problem with many vehicles in a stream of traffic, say, on a link, was not made. The present paper, therefore, develops a simulation model with various types of vehicular interactions, including lane changing, and performs certain verification checks. The results show that the simulation behaves rationally giving credibility to the approach introduced. Although a number of comparisons with empirical observations are made in the paper, complete validation and experimentation are left for further work. Furthermore, the paper draws research attention to the area so that various existing car-following models can be modified in a similar way to mimic non-lane-based car following in multilane traffic flow. Potential practical implication of the work for traffic engineers is mainly capacity assessments especially in places where the discipline of lane-based-driving is weak.