The analysis and certification of parts manufactured through Fused Deposition Modeling and reinforced with short fibers are the main drawback of the emerging technology. The present work builds a framework for the discrete modeling of these parts through the construction of a Representative Volume Element on the mesoscale, which will account for the properties of the material and the features of the manufacturing process and can be used as a building bloc on the mesoscale. To this end, a study conducted in two main steps has been performed: a first analysis of the Representative Volume Element on the microscopic scale of a short fiber embedded in a matrix has been conducted. Studies in convergence ensured the use of optimal mesh and an analysis of orientation determined the reliability of coupling numerical stiffness with orientation averaging, as well as the closure approximation used. The second step consisted of building a Representative Volume Element on the mesoscopic scale, containing the homogenized microscopic oriented stiffness and taking into consideration fibers' distribution and void. The accuracy of the study and carry through of the periodicity and stiffness application were assessed through the comparison of the numerical stiffness tensors with the analytical solution and the stiffness obtained from a unit cell with the resulting one from a periodic structure. An initial framework has therefore been established that takes a minimal input in properties from the microscale and delivers an averaged oriented stiffness tensor on the mesoscale.