A rail fastener includes a rail plate and a rigid stop for rail. The rail plate consists of two parts having a plane surfaces for supporting the rail and extended upward appendages bearing preferably inclined surfaces which cooperate with inclined surfaces of the rail. Each of the parts of the rail plate is placed from opposite lateral side of the rail and they both are tightened with the rail. After they are jointed, the rail fastener becomes as a single whole with rail. One of the parts of the rail plate has a recess one wall of which may be inclined. The rigid stop is mounted in advance into the support structure. When the rail with a rail plate is placed on the support structure, the recess in the rail plate straddles the rigid stop. Then a wedge is mounted into this recess. One of its ends contacts with rigid stop, other which is inclined contacts with inclined wall of the recess in the rail plate. The wedge is bolted to the support structure and pulls up the rail to the rigid stop. As two rigid stops may be mounted in one support structure in advance, their surfaces for contact with rail maintain the gage of the track, and this gage may be maintained with any required accuracy. If for any reason the gage of the track has to be adjusted, the eccentric rigid stop can be used.