The geometrical nonlinear finite element analyses of an elasto-plastic plate subjected to alternately repeated shear force are performed to investigate the mechanical characteristics of the energy absorption steel panels in the hysteretic dampers of a building frame. In the analysis, i) Mindlin plate theory is employed. ii) h-adaptive mesh refinement method is used in generating element division. iii) the stiffness of section is evaluated by the laminated subdomain method, and iv) out-of-plane shear deformation and cyclic work hardening characteristics are considered. The results obtained in the present study are summarized as follows: 1) Using the present error estimation and mesh refinement procedures, although relative error in total tends to increase according as the number of element increases, the deflection and stress resultant converge to exact solution satisfactorily. 2) In accordance with increasing aspect ratio of the plate, the central deflection, caused by plastic shear bucking, tends to decrease. 3) If the width-to-thickness ratio of the plate is set less than 20, it is possible to prevent the plastic shear bucking and the deterioration of its hysteresis loop under cyclic shearing.