This paper describes a numerical study that investigates the effects of loading a lug with a pin. In this work, the loading direction is axial with respect to the lug. The models are both two-dimensional (2D) and three-dimensional (3D). The effects of a change in the level of pin interference, the amount of material around the pin hole, and the thickness of the lug are demonstrated and discussed. Through-thickness effects are shown to be appreciable, and a simple 2D model can give a potentially serious underestimation of the true stress levels which may be particularly significant when a joint is subjected to fatigue loading.