In the Fused Filament Fabrication (FFF) 3D printing process, a structure is created by depositing molten thermoplastic strands layer by layer. Both, self-performed tensile tests and examples from the literature, show that the macroscopically observed material behavior of the test specimens made from polylactic acid (PLA) is strongly influenced by the orientation of the deposited strands to the tensile direction and the ply layup sequence of printing directions. This behavior is governed by local damage processes in the mesostructure. Due to the printing process, voids are present in the printed structure between adjacent strands. These voids mainly cause the observed inhomogeneous material behavior. A finite element model is presented that can predict the macroscopic behavior of tensile loaded structures for arbitrary ply layups. The idea is to represent the individual printed strands with solid elements. These elements exhibit orthotropic elastic material behavior. The corresponding elastic material parameters are obtained by homogenizing the response of the actual strand cross-section with isotropic elastic material. The fracture mechanisms that the model is intended to represent are the failure of the interface between neighboring strands and the tearing of individual strands. These mechanisms are modeled by interface elements with cohesive zone material law, that are located throughout the model between adjacent strands and within the strands. It is shown how the parameterization of the interface elements can be determined based on experimental results and by numerical fitting. Some parameters are highlighted that strongly influence the macroscopically observed behavior. This also gives an indication of the influence that certain FFF printing parameters can have on the material behavior. The numerical model can be used to reproduce the mechanical behavior of FFF printed test specimens for various ply layups. In addition, the fracture patterns, which look different for different ply layups, can also be reproduced.