Materials manufactured by additive manufacturing processes based on extrusion of polymer are recent and difficult to model due to their complex and irregular mesostructure. In the case of printed material with parallel extruded rasters, the existing models, based on 2D Representative Volume Elements (RVEs), neglect the influence of the variation of the cavity shape along the printing direction due to printing irregularities such as ghosting or rippling. In this paper, the mesostructure of the printed material is investigated based on X-ray tomography, and a new approach to extract a 3D RVE is proposed. The new method provides typical mesostructural features of interest, and, in particular, the defects induced by printing irregularities. This method is used to define RVEs for different mesostructures associated with different printing conditions. A numerical homogenization of the printed material based on these RVEs is performed using the Fast-Fourier Transform (FFT) method to determine its macroscopic properties. Both macroscopic elastic properties of the printed material and stress concentrations in the mesostructure are studied and compared to estimate the influence of the different typical mesostructures on the mechanical behavior of the printed material. The results establish a significant influence of the variation of the mesostructure induced by the printing conditions on the rigidity of the printed material, showing the efficiency of the method to better predict the structure– properties relationships of material extrusion additive manufacturing (MEAM) based material. Furthermore, the method links the mesostructural defects to the induced stress concentrations in the mesostructure, thus to their criticality to the resistance of the material.