In this work, unidirectional (UD) fiber-polymer composites were investigated using the finite element analysis. Quadratic, hexagonal and randomly generated fiber arrangements were numerically simulated as unit cell models in the finite element program Abaqus CAE. By applying strain loads in different directions, stiffness and stress components were calculated and compared with macroscopic approximations from a homogenized material model using the Mori-Tanaka method. A self-developed user interface in Python enabled the input of model parameters and various ways to visualize the simulation results. Thus, vivid graphics of stiffnesses, stress components and stress invariants such as the von-Mises stress and the maximum principle stress could be created and analyzed. The simulation results of the stiffnesses of randomly generated cells and the stress components that are normal to the load direction agreed well with the Mori-Tanaka results. It has been shown that stress-unfavorable spots can occur in cells with random fiber arrangements, which are not present in idealized unit cell models like the quadratic or the hexagonal cell. At normal and shear strains of 1% in different directions, a UD glass-fiber-reinforced epoxy resin with 60% fiber volume fraction and random fiber arrangement has stress peaks in the matrix which lie above the yield strength of the used epoxy resin.