Stereoscopic motion images are able to provide observers with realistic and immersive viewing experience. However, observers often experience visual discomfort during the viewing process. In this paper, we investigated the relationship between visual discomfort and the planar motion at different depth levels. The Paired Comparison method was used in the subjective experiments to allow for a precise measurement. The experimental results indicated that the relative angular disparity between foreground object and background played a more important role in determining the visual discomfort than the vergence-accommodation conflict. Furthermore, the results showed that with the increase of planar motion velocity, viewers might experience more visual discomfort. To quantify the effects of relative angular disparity and velocity on visual discomfort, two visual discomfort models were constructed. The preferredmodel was chosen based on the performance as well as the algorithmic complexity. This model can be used as an index for other related researches.