Nowadays, composite materials are widely used in different industries, especially in aerospace structures, due to their particular properties like high specific stiffness and strength. One of the most popular types of composites is unidirectional fiber reinforced composites that offer high tensile strength along the fiber direction. Nevertheless, it was observed that the longitudinal compressive strength of such composites is 50-60% of their tensile strength. The most common failure mode of fiber reinforced polymer composites under longitudinal compression is kink-band formation. It causes a significant drop in the load-bearing capacity of the material. It has been shown that manufacturing defects, particularly fiber misalignment, can be the primary cause of fiber kinking and the final failure of the composite. Since experimental determination of the mechanical behavior of composites costs a lot, and because of the availability of more accurate and faster computational tools in recent years, numerical simulations, especially employing finite element methods, have become attractive. In this study, the goal is to present a two-dimensional micromechanical model for investigating the effect of fiber waviness on the behavior of unidirectional fiber reinforced composite under longitudinal compression. In this modeling, the fiber fracture, the matrix plasticity and damage, and the fiber-matrix interface crack are considered. With this model, the predicted longitudinal compressive Young's modulus, longitudinal compressive strength, and the failure pattern for AS4/8552 UD-CFRP are in good agreement with experimental results. It concludes that the increase of fiber waviness angle leads to a significant strength reduction in fiber orientation. However, the longitudinal compressive Young's modulus is less affected by the fiber misalignment angle. Besides, initial fiber misalignment and matrix shear are detected to be the main factors affecting kink-band formation. Damaged fiber-matrix interfaces can result in matrix failure initiation, and consequently, the final failure of the composite is accelerated, while fiber fracture has a minor effect on the compressive failure of the composite. The parametric study on fiber volume fraction shows an increase of this parameter can improve both the longitudinal compressive Young's modulus and strength. Keywords: Unidirectional fiber reinforced composite, Longitudinal compression, Fiber waviness, Compressive strength, Finite element method.