Evaluation of bi-directional characteristics of base-isolation devices is a very important issue for base-isolated structures. This paper describes a bi-directional loading test of U-shaped steel dampers widely-used for energy dissipation in base-isolated structures. The major findings obtained from the test are as follows: (1) torsion-induced residual deformation leads to contact with damper connections; (2) evaluation method of cyclic deformation capacity, which divides bi-directional orbit into deformations in 0 and 90 degree, is proposed and the validity is verified; (3) cyclic deformation capacity is reduced by cumulative torsion; (4) two indices J c and J f proposed in this paper can evaluate the limitation of cumulative torsion until contact with connections and the tendency of torsioninduced reduction of cyclic deformation capacity.