An elastic under-rail pad, made of an elastic plastic or rubber, has two opposite sides. At least one of its opposite sides presents a surface which at least partly is defined at least approximately by a simple sinusoidal or cosinusoidal trigonometric function or by a composite sinusoidal and cosinusoidal trigonometric function, so that at least on a part of one of the two opposite sides of the elastic pad there are formed protrusions (3) and cavities (4) arranged alternately and changing softly into one another. The elastic pad is used mainly in permanent ways of rail transport as an element attenuating vibrations and absorbing dynamic loads transmitted by railway vehicles to underlying rails.