Fused Filament Fabrication (FFF) is one of the most extensive additive manufacturing technologies for printing prototypes or final parts in various fields. Some printed parts need to meet structural requirements to be functional parts. Therefore, it is necessary to know the mechanical behavior of the printed samples as a function of the printing parameters in order to optimize the material used during the manufacturing process. It is known that FFF parts can present orthotropic characteristics as a consequence of the manufacturing process, in which the material is deposited layer by layer. Therefore, these characteristics must be considered for a correct evaluation of the printed parts from a structural point of view. In this paper, the influence of the type of filling pattern on the main mechanical properties of the printed parts is analyzed. For this purpose, the first parts are 3D printed using three different infill patterns, namely grid, linear with a raster orientation of 0 and 90°, and linear with a raster orientation of 45°. Then, experimental tensile tests, on the one hand, and numerical analyses using finite elements, on the other hand, are carried out. The elastic constants of the material are obtained from the experimental tests. From the finite element analysis, using a simple approach to create a Representative Volume Model (RVE), the constitutive characteristics of the material are estimated: Young’s Moduli and Poisson’s ratios of the printed FFF parts. These values are successfully compared with those of the experimental tests. The results clearly show differences in the mechanical properties of the FFF printed parts, depending on the internal arrangement of the infill pattern, even if similar 3D printing parameters are used.