In this study, vibrations of two bolted flange-connected cylindrical shells are investigated based on three-dimensional elasticity theory. In the semi-analytical model, a set of artificial linear springs—along longitudinal, circumferential, and radial directions—is placed between each pair of grid points employed in the generalized differential quadrature method, which are located on the corresponding flange surfaces. These springs are updated using a genetic optimization algorithm. The primary structure is modeled by dividing it into several shells and assembling them through direct imposition of displacement and stress continuity conditions. In addition, finite element simulations of bolted connections and experimental modal tests are developed to examine vibrational behavior more accurately. Modal analysis in finite element software is inherently linear. Thus, to simulate connections, static analysis results—including stresses from pre-tension torque, deformations, and changes in contact configuration—are used as initial conditions in the modal analysis, enabling simulation of mode shapes of the bolted structure. Natural frequencies obtained from the semi-analytical method, experimental modal testing, and finite element analysis are compared for two connection cases with ten and twenty bolts. The proposed model simulates vibrations of an ideally fabricated bolted flanged cylinder according to the presented procedure with satisfactory precision. However, alternative flange manufacturing methods that may introduce thermal residual stresses or modify mechanical properties warrant separate investigation