A finite element model is developed to study the stresses in a uniaxially loaded infinite sheet containing an interference-fit fastener. The sheet-fastener interface is modeled using one-dimensional gap elements. The geometry is chosen so that the performance of the gap element can be compared with known theoretical solutions. The fastener is modeled as a disk with thickness equal to that of the sheet. The effect of the fastener exiting the sheet, referred to as edge-stiffening, is neglected in the current study. Plane stress conditions are assumed for the sheet and fastener. Material response is assumed to be elastic after fastener insertion and during subsequent loading. Frictionless and no-slip conditions for the sheet-fastener interface are investigated. These two idealized conditions are expected to bracket the real behavior of the sheet-fastener interface. The ability of the gap element to predict the sheet-fastener separation stress for frictionless and no-slip interface conditions is investigated. Results obtained from the finite element models compare favorably with theoretical solutions.