Coarctation of the Aorta (CoA) is a cardiac defect that re- quires surgical intervention aiming to restore an unobstructed aortic arch shape. Many patients suffer from complications post-repair, which are commonly associated with arch shape abnormalities. Determining the degree of shape abnormality could improve risk stratification in recom- mended screening procedures. Yet, traditional morphometry struggles to capture the highly complex arch geometries. Therefore, we use a non- parametric Statistical Shape Model based on mathematical currents to fully account for 3D global and regional shape features. By comput- ing a template aorta of a population of healthy subjects and analysing its transformations towards CoA arch shape models using Partial Least Squares regression techniques, we derived a shape vector as a measure of subject-specific shape abnormality. Results were compared to a shape ranking by clinical experts. Our study suggests Statistical Shape Mod- elling to be a promising diagnostic tool for improved screening of complex cardiac defects.