Fasteners in assemblies are often subjected to multi-axial loading; however, the role of load angle and the assembly design/geometry on the failure of fasteners are not well understood. Existing experimental data often convolutes multiple sources of uncertainty. Thus, numerical modeling is needed to make accurate conclusions about the failure mechanisms of fasteners. This paper investigates the mechanics that controls the loading angle effects on the mechanical response of fasteners by using a simple finite element bolt model without threads. The material model of this model is calibrated against tensile testing data, which minimizes the contribution of the fixture to the bolt's response. The calibrated material model is then used to investigate the loading fixture effects (including the fixture gap, compliance, and double shear loading configuration) on the mechanical response of the fasteners. After identifying the fixture parameters that the fastener's response is most sensitive to, a model of a simplified fixture is validated against experimental results. This investigation reveals that the loading angle effects and most of the loading fixture effects on fasteners' mechanical response are attributed to the change of stress concentrations at the contact tips. The primary contributions of this paper are novel insights into the failure mechanisms of fasteners, and that a reduced model of a fastener can be used to predict its constitutive behavior accurately.