Previous studies have revealed that the change in aerodynamic drag on a test automobile under a parallel running condition is mainly because of the pressure effect, which is caused by the pressure field of the parallel running vehicle, and the effect of the change in wind direction caused by the parallel running vehicle. Apart from the drag change, which can be estimated by assuming a uniform crosswind, the change in wind direction has other effects. In this study, to clarify the other effects, the differences in the wake vortices associated with the change in drag between parallel running and uniform crosswind conditions were identified from the numerical simulation results. The surface pressure on the back excluding the pressure effect under the parallel running condition was lower on the opening side than that under the uniform crosswind condition. In addition, the wake vortices near the region of low surface pressure and their related vortices were focused. Visualizing the flows related to these vortices indicates that the non-uniformity of the flow along the upstream side and the strengthening of the entrainment at the rear end owing to the interference affect the change in the drag in the parallel running condition compared with the uniform crosswind condition. These results are useful for developing control methods to suppress the increase in drag in the parallel running condition.