The current work presents a hybrid Finite Element Method and Discrete Element Method (FEM-DEM) strategy, which combines classical finite and discrete element methods in a common tool, and illustrates its capabilities in reproducing the real behavior of masonry during experimental quasi-static tests and seismic actions. The numerical implementation is available in the open-source LMGC90 code. In this hybrid approach, anisotropic damageable deformable blocks interact each other through contact joints governed by frictional cohesive behaviors. The DEM framework permits large displacements, rotations, and complete detachments of the blocks, which is usually neglected with FEM models. A comparative work is developed with a focus on the advantages and disadvantages of the hybrid model with respect to FEM micro-and macro-modeling (aka block based description or continuous homogeneous description), and DEM using rigid blocks. In this regard, validations through experimental benchmarks are achieved and the results of a diagonal compression test are discussed. Then, the main application performed in this work concerns the seismic assessment of a masonry cross vault. The key aspect of the numerical results concerns the ability of this approach in providing realistic prediction of failure mechanisms, which are relevant for retrofitting works, according to the real cracking pattern, considering the real stereotomy of the masonry and large deformations.