Process for constructing a volume mesh of a subsurface formation comprising at least one sedimentary layer traversed by at least one fault.On the basis of a representation in a closed domain of the geometry of the horizons and of the faults in a parametric space before deformation and rupture, the bounds of the blocks delimited by the faults, the horizons and the boundaries of the domain are projected onto a reference surface. Next a surface mesh is constructed constrained by the projections thus obtained on the reference surface. At each node of the surface mesh, a vertical polygonal line passing through this node is defined. Next a volume mesh is constructed by vertical extrusion of the surface mesh along the polygonal lines.Application in particular to exploration and to exploitation of oilfields.