The invention relates to a ballastless track section for a rail vehicle, said section being fastened to a platform (10) and comprising: a prefabricated concrete track slab (20, 120) comprising two stringers (21, 22); a rounded bearing surface (21c, 22c) borne by an underside of each stringer at each longitudinal end and having a curvature, the center of curvature of which is the top of a rail (21b, 22b) borne by the stringer; a prefabricated support pad (30, 130) for supporting each longitudinal end of the slab (20, 120) and comprising at least two support bases (33, 34) for the two stringers of this longitudinal end of the slab, each base (33, 34) comprising at least one shim (33a, 34a) of predetermined thickness supporting said rounded bearing surface (21c, 22c) of the stringer of said slab facing this base.