In Roman Baths, the Romans employed barrel and groin vaults of great dimensions, with maximum span more than 20 m; simple tools of structural analysis of ancient wide span vaulted halls are still lacking, due to geometrical and material complexity. In this paper, we study the collapse behavior, under horizontal static action, of a corner cross vault of the Baths of Diocletian in Rome (Hall I). Two methods of analysis are here used: non-linear incremental finite element and limit analysis. In both cases, 3D models have been developed by means of UAV inspection, NDT measures, and AVT monitoring. The construction of the overall 3D geometry has been here afforded with a specific pre-processing approach. Midas commercial software has been employed for FEM analysis, assuming a constitutive law specifically developed for Roman concrete. In limit analysis, masonry is discretized as a system of interacting rigid bodies in no-tension and frictional contact. The computational code consists in a linear approach, which makes use of a series of optimization packages via lower and upper bound techniques. Finally, a strategy based on FEM analysis including discontinuities was implemented, and the results were compared with the two previous approaches.