Fused filament fabrication (FFF) is one of the most commonly practiced additive manufacturing (AM) processes. Lately, FFF is used in big area additive manufacturing (BAAM) with potential industrial use and is getting popular for several daily-life applications due to its low-cost nature. However, there are many challenges faced by FFF process with the most prominent examples being ability to produce stronger parts, general understanding of mechanics going into the process, and limited printing envelope. Most of these barriers prevent the adoption of FFF as a full-scale industrial process at the moment. One of these challenges is the ability to predict mechanical behavior of the printed parts under external loads which is crucial to any engineering design and is an obstacle for the FFF-made parts. This thesis reports the application of asymptotic homogenization as a tool for predicting the mechanical properties of FFF-made thermoplastics with line infill, grid infill, and fiber-reinforced cases. Accurate prediction of mechanical properties would allow engineers to use material properties in finite element packages for design and analysis purposes. Furthermore, engineers would potentially be able to predict mechanical properties directly from the slicing software and thus be able to optimize mechanical performance, material usage, and printing time. Therefore, the main contribution of this research is to help engineers predict mechanical behavior of 3D printed parts thus facilitating the adoption of FFF technology as an industry-accepted manufacturing process in practice.