Reservoirs lined with concrete slabs are very common in the northern cold regions of China. Failures such as the rotation and the dislocation of concrete lining slabs are usually found in those ice-covered reservoirs each year in winter. In this study, the interaction processes between water, ice, and lining when water level changes in ice-covered reservoirs are evaluated based on the theory of beams on elastic foundation. In general, ice cover can generate a rotation effect (bending moment) on concrete lining slabs when water level changes in ice-covered reservoirs. Under such conditions, the bending moment at the ice edge increases with the increase of the ice cover width and thickness. Once the tensile stress at the interface between concrete slab and its base layer exceeds the tensile strength of the interface itself, the concrete slab separates from its base layer and the support condition of the ice cover changes from fix-supported to hinge-supported. Then the rotational failure of the concrete slab may occur due to the rotation effect acted by ice cover. The calculated rotation angle of the concrete lining slab is in agreement with the angle observed at a reservoir in northwest China. In addition, prevention measures such as concrete lining slabs with hydrophobic coating on the surface, concrete lining slabs with dark surface, anchoring concrete slabs to reservoir slope, and integral large-scale lining modules are proposed to mitigate such rotational lining failures in ice-covered reservoirs. The results can help to improve the performance and service life of reservoirs in cold environments.