Composites are used in assemblies more often now, requiring different joints such as mechanical fasteners, riveting, welding, and polymeric adhesives. These methods tend to trade off on the strength of the joint for increased assembly weight and cause additional constraints to be considered in the design process, complicating the design process further. An optimal candidate would be one that could provide high strength to weight ratio with minimal hassle for maintenance and high fatigue performance. One such candidate is stitch-bonded composites. Despite several experimental investigations on the material behaviors of these composites, the corresponding material response models are still far from maturity. The problem statement of this paper is to simulate and compare the delamination damage in an unstitched adhesively-bonded joint, a stitch-bonded joint, and a bolted joint of a four-layer carbon fiber epoxy composite laminate using a finite element model developed for all cases. The stitching thread considered in the model is made of Vectran liquid crystal polymer spun fibers and has been treated as one-dimensional truss elements embedded into a lap joint. The delamination failure was modeled as inter-laminar failure using a cohesive zone method. The debonding between the stitching thread and the surrounding material (i.e., epoxy and carbon fiber) was not modeled. The crack opening mode or Mode I delamination was observed for the lap joint. The simulation results include the stress and strain fields, critical strain energy release rates, and the load-displacement curves for all considered joint types. The results provided us better insights into the inter-laminar interaction when delamination occurs and the mechanisms with which the stitching arrests the propagation of the bond failure.