Oriented matroid theory provides a combinatorial encoding of convexity properties, and of relative positions, in a finite set of geometrical points. One can see it as yielding a discrete notion of shape, that is structural and not based on numerical measures as usual. We use it as a framework for a method to investigate, classify and characterize the shapes of 3D landmark-based models. This morphometry method will be illustrated on sets of skull shapes coming from various species or presenting various types of clinical deformations, for applications in physical anthropology or in 3D medical image analysis (from a joint work with Kevin Sol and Gérard Subsol).