This study aims to determine the finite element analysis of a BSPD-SHS (bi-directional shear panel damper with a square hollow section) device, to dissipate the seismic excitation energy through the lateral relative displacement between the pier and girder of the simple support bridge. The configuration of the square hollow section is also performed for a double role, such as web panel and flange, indicating the expectations to reduce the seismic force within the lateral and longitudinal directions. In the preliminary development phase, the finite element analysis was conducted under monotonic loading, to examine the skeleton curve characteristics and internal stress action on resisting seismic force. The characteristics of this curve include elastic stiffness, shear strength, post-yield behavior, and internal stress distributions. Based on the evaluation of the BSPD-SHS slenderness effect, the variation of depth-thickness ratio was considered between 25 to 67. To investigate the fitness of the theoretical shear strength formulation, two different hardening roles of the metal plasticity model were subsequently compared in this study, including the elastic-perfectly plastic and isotropic/kinematic techniques. Furthermore, the effect of the restrained degree of freedom idealization on the top base plate was captured. This indicated that all specimens model with the restrained top base plate achieved stable post-yield stiffness. In implementing the unrestrained top base plate, this stiffness was achieved when the web slenderness ratio equaled 25. The differences observed between the hardening roles also generated a slight yield shear strength discrepancy. However, significant differences occurred in the post-yield shear strength. The shear resistance proportion of the stress components was also accurately quantified with an analytical stress integration. Based on the restrained top base plate, the flange tension field generated a significant contribution to the post-yield shear resistance.