The energy dissipation devices play a crucial role to mitigate the impact of dynamic loads on structures. This study investigates a superelastic shape memory alloy U-shaped damper (SMA-UD) with a self-centering (SC) function. The working principle of the SMA-UD in both active and passive states is elucidated, highlighting the conversion of shear deformation between parallel legs into flexural deformation under cyclic loading. Two finite element tools, ABAQUS 6.14 and SAP 2000, are employed for a comprehensive analysis. A three-dimensional finite-element (FE) numerical simulation was conducted, demonstrating close agreement with existing experimental and numerical results. Mechanical properties of SMA-UD including ultimate force and energy-dissipation capability were compared using the two problem-solving tools under identical cyclic loading conditions. The numerical findings reveal stable flag-shaped hysteresis loops and excellent self-centering (SC) ability in both solvers, with nearly symmetrical strength observed in positive and negative loading directions. This study contributes valuable insights into the performance of SMA-UDs, emphasizing their potential for self-centering applications in structural engineering.