A stratified-structure laminar covering material, which can be used for example as a flooring for sports facilities, comprises an outermost layer, a bottom layer, and an intermediate layer set between the outermost layer and the bottom layer. The aforesaid layers comprise a matrix constituted by a mixture of polyolefin and thermoplastic elastomer, the matrix being substantially identical for all three layers. The matrix of the outermost layer is substantially free from fillers and has a first value of density. The bottom layer contains fillers so as to have a second value of density greater than said first value of density, and the intermediate layer contains fillers so as to have a third value of density intermediate between the first value of density of the outermost layer and the second value of density of the bottom layer.