Process for modelling a sedimentary basin, said sedimentary basin having undergone a plurality of geological events defining a sequence of states of said basin, by means of a digital basin simulation executed on a computer, said digital basin simulation solving at least one poromechanics equilibrium equation according to a face-based smoothed finite element method in order to determine at least one strain field and one deformation field, characterized in that the process comprises implementing at least the following steps: A. measurements are made of physical quantities relating to said basin by means of sensors, and a first meshed representation which is representative of said basin is constructed for each of said states of said basin, said first meshed representations of said basin for each of said states being predominantly formed by hexahedral meshes; B. by means of said digital basin simulation and said first meshed representations for each of said states, at least one deformation field and one strain field are determined for each of said states by applying at least the following steps for each of said first meshed representations of said states: a) a second meshed representation of said state is determined by subdividing each of said hexahedral meshes of said first meshed representation of said state into six pyramidal meshes, said non-hexahedral meshes of said first meshed representation being unchanged in said second meshed representation; b) said basin is modelled by determining at least said displacement field and said strain field for said state by means of said digital simulation applied to said second meshed representation of said state. A. measurements are made of physical quantities relating to said basin by means of sensors, and a first meshed representation which is representative of said basin is constructed for each of said states of said basin, said first meshed representations of said basin for each of said states being predominantly formed by hexahedral meshes; B. by means of said digital basin simulation and said first meshed representations for each of said states, at least one deformation field and one strain field are determined for each of said states by applying at least the following steps for each of said first meshed representations of said states: a) a second meshed representation of said state is determined by subdividing each of said hexahedral meshes of said first meshed representation of said state into six pyramidal meshes, said non-hexahedral meshes of said first meshed representation being unchanged in said second meshed representation; b) said basin is modelled by determining at least said displacement field and said strain field for said state by means of said digital simulation applied to said second meshed representation of said state. a) a second meshed representation of said state is determined by subdividing each of said hexahedral meshes of said first meshed representation of said state into six pyramidal meshes, said non-hexahedral meshes of said first meshed representation being unchanged in said second meshed representation; b) said basin is modelled by determining at least said displacement field and said strain field for said state by means of said digital simulation applied to said second meshed representation of said state.