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SUMMARY Horizontal bidirectional loading tests are conducted for real‐sized high‐damping rubber (HDR) bearings with diameters of 700 mm (HDR700) and 1300 mm (HDR1300). The hysteresis loops of these bearings under bidirectional horizontal loadings are compared with those under unidirectional loadings. The results show that the bearing force measurement in the primary direction of loading increases when there is displacement in the orthogonal direction. Unusually, the maximum restoring force in the orthogonal direction to the primary loading direction occurs near zero displacement. On the basis of the observations of the restoring forces, a rate‐independent model is proposed. This model simulates well the test results under both bidirectional loading and unidirectional loading. It can reproduce the irregular restoring forces characteristics around zero displacement as described above. Bidirectional loading induced twist deformation in the HDR bearings that increased local shear strains. This phenomenon results in an early failure as observed in HDR700. The additional shear strain is estimated based on the twist deformation measured by video image analysis. The comparison of the nominal total shear stress demonstrates that the increase of shear stress because of bidirectional loading occurs when the average shear strain is larger than about 200%. The larger the shear strain, the greater the bidirectional effect. It is shown that the nominal total shear stress of average strain of 350% under bidirectional circular loading pattern is approximately the same as the average shear strain of 400% under unidirectional loading. This means that the average shear strain of 350% under a bidirectional circular loading corresponds to a local shear strain of 400%. Copyright © 2012 John Wiley & Sons, Ltd.