New software, called Marbles, is introduced that employs SAXS intensities to predict the shape of membrane proteins embedded into membrane nanodiscs. To gain computational speed and efficient convergence, the strategy is based on a hybrid approach that allows one to account for the contribution of the nanodisc to the SAXS intensity through a semi-analytical model, while the embedded membrane protein is treated as a set of beads, similarly to as in well known ab initio methods. The reliability and flexibility of this approach is proved by benchmarking the code, implemented in C++ with a Python interface, on a toy model and two proteins with very different geometry and size.