The present invention relates to a device for absorbing the vibration of a rail, the replacement of which is easy. The device comprises a support plate (8) having an anchor hole (8a) for a stay anchor; a thick vibration absorbing pad (1) having an anchor hole (1a); a support plate for the rail (2) having an anchor tube (2b), and a fixing hole (2c) formed at the anchor tube (2b), said fixing hole being formed through the support plate for the rail (2) in parallel with the direction in which the rail is laid, as well as a stay anchor (4) with a fixing nut (5) engaged with the thread (4a) provided at the upper end of the stay anchor (4); and a cap (7) for protecting the fixing nut (5). The present invention also provides a pad which is divided into a main body (1-1) and a corner portion (1-2) by the means of the boundary line which is cut diagonally at the inward portion of the center of the anchor hole (1a).