The invention relates to an elastically deformable composite material suitable to be processed further into sheet-like abrasive products, comprising a sheet-like supporting base coated or impregnated with a prepolymer material which obtains thermosetting properties when thermally post-cured, or consisting of a coated or impregnated supporting base, characterized in that the supporting base comprises at least one layer of bonded fibers selected among inorganic fibers and organic synthetic fibers, if necessary mixed with natural fibers. Moreover, it relates to a method for the manufacture of the composite material.