The invention relates to a system for fastening a rail (S), comprising a sleeper (1) which has a supporting face (3) intended to support the flange (Sf) of the rail (S), the supporting face (3) merging, at its sides which extend parallel to the longitudinal extent (L) of the rail (S) to be fastened thereto, into respective levelling faces (7, 8) which are situated at a higher level than the supporting face (3), an angled mounting plate (20, 21) which has, in each case, a central portion (22), on the underside (23) of which is formed a support surface (24) by which the angled mounting plate (20, 21) can be placed down on the respective levelling face (7, 8) assigned to it of the sleeper (1), and a supporting portion (25) which is formed onto the central portion (22) and points downwards from the underside (23) of the latter and which, when the system is fully fitted, bridges the clear space between the flange (Sf) of the rail (S) and the levelling face (7, 8), a resilient member (100, 101) which can be placed down on the angled plate (20, 21) and which has, in each case, two holding arms (105, 106) by which, when the system is fully fitted, the resilient member (100, 101) exerts a holding force (H) on the rail (S), and a clamping member (P) which, when the system is fully fitted, exerts a clamping force (F) on the resilient member (100, 101). Such a system achieves an improved ability to be permanently loaded and exhibits a prolonged lifetime at reduced production costs, in that according to the invention when the system is fully fitted, the axis (W) along which the clamping force (F) exerted by the clamping member (P) acts passes through the levelling face (7,8).