A seismic-resistant fluid reservoir cover includes a plurality of panels and a network of flexible membranes coupled to adjacent panels. The flexible membranes are made of a potable water approved material, and the panels and the membranes create a fluid tight seal. Each panel in the reservoir cover is able to move along three directional axes independently of the adjacent panels while maintaining the fluid tight seal, at least in part because of the flexibility or the slack in the flexible membrane. A support member, such as a backer rod, may also be positioned in the spaces between the panels.