Asbestos-free organic friction material, in particular for producing brake pads and shoes for vehicles made up of a composition or mixture having a fibrous base, a filler, and an organic binder. The composition is completely free of copper and copper compounds or alloys and includes in the fibrous base, together with inorganic and/or organic fibers, from 1% to 10% by volume, calculated relative to the total volume of the composition, of stainless steel fibers.