The G protein-coupled receptor (GPCR) superfamily is a large group of membrane proteins which, because of their vast involvement in cell signalling pathways, are implicated in a plethora of disease states and are therefore considered to be key drug targets. Despite advances in techniques to study these receptors, current prophylaxis is often limited due to the challenging nature of their dynamic, complex structures. Greater knowledge and understanding of their intricate structural rearrangements will therefore undoubtedly aid structure-based drug design against GPCRs. Disciplines such as anthropology and palaeontology often use geometric morphometrics to measure variation between shapes and we have therefore applied this technique to analyse GPCR structures in a three-dimensional manner, using principal component analysis. Our aim was to create a novel system able to discriminate between GPCR structures and discover variation between them, correlated with a variety of receptor characteristics. This was conducted by assessing shape changes at the extra- and intracellular faces of the transmembrane helix bundle, analysing the XYZ coordinates of the amino acids at those positions. We have demonstrated that GPCR structures can be classified based on characteristics such as activation state, bound ligands and fusion proteins, with the most significant results focussed at the intracellular face. Conversely, our analyses provide evidence that thermostabilising mutations do not cause significant differences when compared to non-mutated GPCRs. We believe that this is the first time geometric morphometrics has been applied to membrane proteins on this scale, and believe it can be used as a future tool in sense-checking newly resolved structures and planning experimental design.