The French territory presents many old historical constructions classified as building open to the public (ERP). However, this architectural heritage in masonry is fragile regarding the fire risk as the disaster that occurred on April 15 at Notre-Dame Cathedral in Paris. After a fire, the heritage value of these ERP implies that, if a doubt of structural stability exists, the question of their demolition is generally ruled out, unlike contemporary constructions without architectural value. Moreover, when these buildings are classified as Historic Monuments (HM), they must be restored and, or at least be rebuilt as it was. In any case, the question of the structure stability subjected to fire remains. However, today, knowledge and tools to assess the post-fire structural stability of a masonry building are still missing. The DEMMEFI project proposes to respond to this problem by carrying out a post-fire structural assessment methodology for complex 3D masonry structures. This methodology will first be applied to a common span of the nave of Notre-Dame cathedral and then generalized to similar masonry historic buildings with high heritage value. The methodology developed will be based on the combined and optimized use of the two main existing numerical methods: the finite element method (FEM) and the discrete element method (DEM). A so-called hybrid FEM-DEM method will be proposed in order to combine the advantages of the FEM and DEM methods in order to simulate the mechanical behavior of masonry material. The problem of mechanical stability subjected to fire action (during fire and post-fire) will be provided by a thermo-mechanical characterization of equivalent materials (limestone and lime mortar) and assemblies. Moreover, an estimation of the spatio-temporal fire action on the vault extrados will be studied. The modeling strategy will be based on a multi-scale approach using the hybrid method from the material to the structure. Finally, the relevance of stability indicators in terms of limit thrusts, limit displacements or limit stresses will be studied for each type of sub-structure of the cathedral in order to propose practical verification methods contributing to the structural assessment of these complex heterogeneous structures.