Abstract : The linear elastic fields occurring in a cementitious material are numerically computed and analyzed in order to determine the spatial arrangement between the microstructure and high- stress regions in the matrix. The microstructure is obtained by segmentation of a mortar sample microtomography whereas fields are evaluated on the 3D image grid using the FFT algorithm for both hydrostatic and shear strain loading. Different contrasts, i.e. ratios of the Young moduli between aggregates and matrix are considered: 10−8, 3, 100, 1000 and 104. Various components of the stress tensor are successively analyzed, corresponding to the component "parallel" to the applied loading and invariant components. Regions of stress concentration are correlated to the skeleton by influence zone of the aggregates phase. Moreover, when hydrostatic strain loading is applied, the highest values of the von Mises component of the stress tensor are both on the aggregates skeleton and at low distance from aggregates. Similar analysis of the local fields are carried out on a simulated microstructure made of boolean random polyhedra and compared with results on the real mortar microstructure.