A compressed slender tubular string inside a rigid wellbore is governed by coupled geometric nonlinearity in buckling and contact nonlinearity, which often causes convergence failure in conventional static analysis. To address this issue, a virtual transient dynamic finite element model is proposed after discretizing the tubular string into elements. A high damping ratio is first introduced to dissipate the system’s oscillatory energy and drive the structural response toward equilibrium, thereby obtaining stable configurations and contact states for different buckling modes. Finite element simulations are then performed to investigate the effects of friction coefficient on critical buckling load, deflection curves, and post-buckling mechanical parameters. The results show that, as the friction coefficient increases from 0 to 0.4, the critical load of the single-helical buckling configuration rises by 92.4%, while the helical orientation angle under a constant dimensionless axial load factor of k = 35 decreases by 37.7%. Friction therefore markedly increases the axial load sustained by post-buckling configurations in continuous contact, suppresses buckling deformation, and produces a clear hysteresis effect during buckling evolution. Friction also significantly affects post-buckling parameters such as bending moment and shear force. This study provides a numerical basis for buckling analysis and engineering control of downhole tubular strings under frictional effects.