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Reinforced Concrete (RC) core walls are widely used to resist lateral loads because of their high flexural and torsional stiffnesses. Their seismic performance parameters, including residual displacement, floor acceleration, and residual in-plane rotation, were examined by many researchers. However, reports from previous earthquakes have highlighted the difficulties of repairs addressing their residual displacements and/or rotations. This paper addresses this problem by investigating the influence of self-centering superelastic shape memory alloy (SMA) bars on the seismic performance parameters of RC core walls. A case study building is analyzed, considering both steel and SMA reinforcement, for unidirectional and bidirectional seismic excitations. Different mass eccentricities are assumed. SMA RC core walls are found to have significantly reduced floor accelerations, residual displacements, and residual in-plane rotations as compared to steel RC core walls.