Bolted flange joints are extensively used in pressure vessels and piping equipment and rotating machinery. Achieving a uniform bolt preload during the assembly process is particularly important to satisfy tightness in applications such as oil, gas, fossil, and nuclear industries. However, this task becomes very difficult due to the need of retightening the bolts because of elastic interaction and bolt cross talk. The risk of leakage failure under service loading is consequently increased because of the scatter of the bolt preload. This article presents an analytical model based on the theory of circular beams on the linear elastic foundation that simulates the elastic interaction present during the tightening of bolted flange joints to reduce the number of passes while achieving bolt load uniformity. As such, a novel methodology that optimizes tightening sequence strategies is suggested to obtain uniform bolt tension while avoiding yield under a minimum number of tightening passes. In this regard, based on the target preload, the load applied to each bolt in each pass is suggested. The developed approach is validated both numerically using finite element method and experimentally on a NPS 4 class 900 welding neck flange joint using the criss-cross tightening and sequential patterns.