Bolted flange joints are widely used to connect pressure vessels and piping equipment together and facilitate their disassembly. Initial tightening of their bolts is a delicate operation because it is extremely difficult to achieve the target load and uniformity due to elastic interaction. The risk of failure due to leakage and fatigue under service loading is consequently increased. This paper presents a study on the effect of elastic interaction that is present during the tightening of bolted flange joints using three-dimensional nonlinear finite-element modeling and experimentation. The nonlinear nonelastic behavior of the gasket is taken into account in the numerical simulation. The scatter in bolt preload produced during the tightening sequence is evaluated. Based on the elastic interaction coefficient method, the initial target tightening load in each bolt for every pass is determined by using the nonlinear finite-element model to obtain a uniform preload after the final tightening pass. The validity of the finite-element analysis (FEA) is supported by experimental tests conducted on a NPS 4 class 900 weld neck bolted flange joints using fiber and flexible graphite gaskets. This study provides guidance and enhances the safety and reliability of bolted flange joints by minimizing bolt load scatter due to elastic interaction.