Abstract: The sleeper (tie) comprises a body which has a variable cross section along its length and is made from reinforced polymer concrete with a dispersed reinforcement in the form of steel or synthetic fibres or both the one and the other together, which fibres compose 5-7% of the total mass of the body of the sleeper, are of different length and have a different percent of content depending on the type of fibre. At the points of fastening the rails, inserts are provided in the body, the height of the inserts satisfying the relationship: 2/3 H.sub.1 .gtoreq.H.sub.2 >1/3 H.sub.1, where H.sub.1 is the height of the highest portion at each end of the body of the sleeper, H.sub.2 is the height of the insert. The upper face of the middle part of the body is positioned higher than the lower face of the insert by a value .DELTA.H which is within the limits 0.5(H.sub.1 -H.sub.2)>.DELTA.H>0.1(H.sub.1 -H.sub.2). Metallic and wooden inserts of various geometric shape are used.