We present ShapeOp, a robust and extensible geometric modelling paradigm. ShapeOp builds on top of the state-of-the-art physics solver (Bouaziz et al. in ACM Trans Graph 33:154:1–154:11, 2014). We discuss the main theoretical advantages of the underlying solver and how this influences our modelling paradigm. We provide an efficient open-source C++ implementation (www.shapeop.org) together with scripting interfaces to enable ShapeOp in Rhino/Grasshopper and potentially other tools. This implementation can also act as a template for future integration of computer graphics research. To evaluate the potential of ShapeOp we present various examples using our implementation and discuss potential implications on the design process.