This dissertation focuses on the hi-fidelity finite element (FE) analysis of laminated composite structures. We start with a brief mention of wound composite modeler (WCM), a toolkit for modeling filament-wound composite overwrapped pressure vessels (COPVs). Several simple numerical examples by WCM verify its useful utilities, but also indicate that discrete damage/cracks cannot be properly modeled by homogenized elements. We then attempt to model a tow break with interfacial cracks in a composite overwrap with traditionally used FE methods, but various kinds of erroneous results are observed, showing that the standard interface elements are not capable of modeling interacting cracks. Therefore, we review and discuss some representative methodologies in the literature for modeling discrete damages in composite laminates, and reveal that the current techniques are not capable of explicitly modeling all three types of failure modes and their interactions in laminated composite structures with arbitrary layup angles. In order to overcome the limitations of existing methods, we present an auto-generated geometry-based discrete finite element model (AGDM). This new approach is realized by in-house developed preprocessing commands, and can be adopted for various applications. Then we demonstrate a FE analysis, in which the predicted damage pattern and tensile strengths of the tested specimens are in excellent agreement with X-ray and data from experimental observations. Finally, we investigate the overload profile around an in-situ tow break in COPVs. Some analytical formulas to evaluate stress concentration factors (SCF) are provided, which are derived from a shear-lag based analysis and stress fields under a point load applied on the surface of a transversely isotropic elastic half-space. Then several FE analysis made possible by AGDM are also presented.