Many important problems in medical imaging require analysing the causal effect of genetic, environmental, or lifestyle factors on the normal and pathological variation of anatomical phenotypes. There is, however, a lack of computational tooling to enable causal reasoning about morphological variations of 3D surface meshes. To tackle this problem, we present the framework of deep structural causal shape models (CSMs) using a database of subcortical brain meshes. CSMs enable subject-specific prognoses through counterfactual mesh generation, by utilising high-quality mesh generation techniques, from geometric deep learning, within the expressive framework of deep structural causal models (DSCM).