An elastic underlayer for floorings, for instance, floorings for sports facilities such as synthetic-grass coverings, comprises a first laminar structure and a second laminar structure that enclose between them pouches filled with granular elastic material. The structures in question comprise a layer of non-woven fabric coupled with a polyolefin layer. The polyolefin layers enclose between them the pouches, which preferably have a parallelepiped shape with a square base, with sides having a length of 20-60 mm, typically 45 mm, and a height of between 20 and 40 mm, typically 30 mm. The pouches are filled with granular elastic material, such as granules of recycled tires having a size of between 0.5 and 7.0 mm.