Bolted joints are widely used to connect structural components in rotating machinery. However, the initial tightening of the bolts is a delicate operation because it is extremely difficult to achieve the target load and uniformity due to elastic interaction. The scatter in the bolt preload has a major impact on the concentricity and consequently the dynamic behavior of rotating machinery. The risk of failure due to vibration and fatigue under service loading becomes an issue. This paper treats the effect of elastic interaction on the eccentricity during the tightening of bolted joints of rotating machinery using finite element (FE) method. In this regard, a two-component bolted flange joint of a high pressure compressor (HPC) of an aero-engine is investigated. The component surface tolerances measured by Rotary Precision Instruments (RPI) are taken into account in the numerical simulation. A method is proposed to calculate the concentricity of components obtained from the radial runout data based on the Least Square method (LSM). The scatter in bolt preload under different interference fit, surfaces tolerance, initial preload, and tightening sequence are evaluated. Furthermore, the influence of these structures and tightening sequence parameters on the concentricity are investigated. The validity of the finite element analysis is supported by experimental tests conducted on scaled specimens of HPC. This study can provide guidance and enhance the dynamic performance of bolted joints for rotating machinery.