This research explores the structural function of early Gothic flying buttresses. Their effectiveness is evaluated under minimum thrust conditions using conventional limit analysis. The significance of various formal characteristics of the flying buttress (length, intrados curvature, thickness, inclination) as well as probable failure modes (sliding and support displacement), are investigated both parametrically and using a series of French and English early Gothic flyers. The results permit us to address certain long-standing art-historical assumptions and demonstrate that the method of study employed holds promise for future exploration for all types of flying buttresses - not just those from the early Gothic period.