Recent advancements in computational methods has led to improvements in the computational modeling of tensile failure of composite laminates. Models for compressive failure however, have not yet reached the same level of maturity. Particularly in the case of fiber kinking there is a need for improved modeling techniques. Fiber kinking occurs when fiber imperfection combined with matrix failure lead to localized deformation in a band of finite width (kink bands). Current computational models have focused on micro-level, where matrix and fibers are modeled independently. The various experimental and analytical research on fiber kinking has lead to numerous failure criteria and analytical models for kink bands. The collapse response of kink bands however, has yet to be incorporated in a meso-level computational model. A step is required to translate these micro-mechanical and analytical models to a meso-level framework and improve the state of the art of compressive failure modeling of composite laminates. In this thesis an attempt is made at transitioning from a micro to a meso-level failure model for fiber kinking. A discontinuous approach is proposed for modeling kink bands. The kink bands are represented as strong discontinuities in the displacement field using the phantom node method. With this method the angle of failure propagation can be easily controlled. The discontinuities are introduced after violation of a stress-based failure criterion and therefore necessitates the use of an initially rigid cohesive law to incorporate the kink band response. To construct such a law a shifted formulation is used, meaning, the law is derived with a finite initial stiffness and shifted to achieve the initially rigid behavior. Strong discontinuity analysis and a discrete micro-mechanical model are used to derive two separate cohesive models in the local kink band coordinate frame, while a simplified approach is also applied to derive a third model in the discontinuity coordinate frame. The nonlinear characteristics and bifurcation of the models necessitate the use of a capable solution algorithm that will follow the true equilibrium path. Therefore the crack opening displacement arclength method is used to; indirectly control direction of crack growth, pass the bifurcation point and capture possible snap-back behavior. Additionally an adaptive time stepping strategy is applied to increase efficiency and robustness. The model and algorithm have been implemented in a one dimensional framework using Timoshenko beam elements and verified against an analytical solution. The local models have shown to capture the trends derived using the analytical solution well, with the strong discontinuity model being the most accurate. The simplified approach however fails to properly account for these trends. The current work has resulted in an initial step towards a meso-level computational model of fiber kinking. It is shown that the discontinuous approach provides a good representation of kink bands provided that a proper cohesive model is used that incorporates both material and geometrical parameters influencing kink bands.