A pool cover has a compressible safety edge providing resilient conformance to obstructions over a wide range of atmospheric and loading conditions. Pool covers can be stretched over the water surface of a swimming pool, extending securely onto the surrounding apron except in the area of poolside obstructions. A safety edge may include a resilient compressible foam core supported and protected by a tough flexible fabric enclosure attached to the edge of the pool cover so as to be held against and conform to the obstruction to secure the opening. Solid or hollow foam cylinders of different shapes may be used and forms of extruded plastic elements are shown.