Geodynamic codes have become fast and efficient enough to facilitate sensitivity analysis of rheological parameters. With sufficient data, they can even be inverted for. Yet, the geodynamic inverse problem is often regularized by assuming a constant geometry of the geological setting (e.g. shape, location and size of salt diapirs or magma bodies) or approximating irregular bodies with simple shapes like boxes, spheres or ellipsoids to reduce the parameter space. Here, we present a simple and intuitive method to parameterize complex 3D bodies and incorporate them into geodynamic inverse problems. The approach can automatically create an entire ensemble of initial geometries, enabling us to account for uncertainties in imaging data. Furthermore, it allows us to investigate the sensitivity of the model results to geometrical properties and facilitates inverting for them. We demonstrate the method with two examples. A salt diapir in an extending regime and free subduction of an oceanic plate under a continent. In both cases, small differences in the model’s initial geometry lead to vastly different results. Be it the formation of faults or the velocity of plates. Using the salt diapir example, we demonstrate that, given an additional geophysical observation, we are able to invert for uncertain geometric properties. This highlights that geodynamic studies should investigate the sensitivity of their models to the initial geometry and include it in their inversion framework. We make our method available as part of the open-source software geomIO.