This paper presents an assessment of a two-scale framework for the study of softening materials such as concrete. The procedure is based on a hierarchical Finite Element (FE) scheme in which computations are performed both at macroscopic and mesoscopic scale levels. The methodology is chosen specifically to remain valid when the scales are coupled. This situation is encountered in fracture processes of heterogeneous materials. The effect of the boundary conditions chosen to construct the meso-scale problem is studied by comparing multi-scale and mono-scale analyses. It is shown that macroscopic mesh size dependence is encountered when using linear interpolated boundary displacements at the interface between meso-specimens. An improvement to the linear interpolated boundary displacements is presented which proves to be more adequate when strain localisation phenomena are encountered at the interface of the meso-specimens. The specific upscaling procedure for the improved boundary conditions remains an issue of ongoing research.