Arrangement for determining the profile of rails in laid track systems with at least one measuring head for measuring a cross-sectional profile of a rail head along a rail path, wherein the measuring head is mounted on a support frame so as to be adjustable with respect to the cross-sectional profile of the rail head, which support frame is movable in parallel along the rail by means of a vehicle guided by the rails for capturing a longitudinal profile of the rail head, characterized in that - the at least one measuring head has a guide profile in the form of an L-shaped profiled rail, wherein the guide profile can be pressed, in a defined manner, to a rail top side and a rail inner side of the rail head, and a measuring head housing which is rigidly coupled to the guide profile and in which at least one measuring probe (36; 37, 38) is adjustably arranged in such a way that the rail head profile is determinable with respect to the guide profile which forms the guide and reference basis for the measuring probe, wherein the length of the guide profile is adapted to the identifiable wear corrugations of the rail head, - a measuring head frame for receiving the at least one measuring head on each side of the support frame is present, wherein - the measuring head frame is adjustable horizontally and transversely to the rail by means of two horizontal linear drives via a horizontal guide on the support frame, in order to move the guide profile relative to the rail inner side of the rail head and to press it over the entire length of the guide profile, and - the measuring head frame has at least one vertical guide and two vertical linear drives for vertical adjustment of the measuring head with respect to the rail, in order to move the guide profile relative to the rail top side of the rail head and to press it over the entire length of the guide profile. - the at least one measuring head has a guide profile in the form of an L-shaped profiled rail, wherein the guide profile can be pressed, in a defined manner, to a rail top side and a rail inner side of the rail head, and a measuring head housing which is rigidly coupled to the guide profile and in which at least one measuring probe (36; 37, 38) is adjustably arranged in such a way that the rail head profile is determinable with respect to the guide profile which forms the guide and reference basis for the measuring probe, wherein the length of the guide profile is adapted to the identifiable wear corrugations of the rail head, - a measuring head frame for receiving the at least one measuring head on each side of the support frame is present, wherein - the measuring head frame is adjustable horizontally and transversely to the rail by means of two horizontal linear drives via a horizontal guide on the support frame, in order to move the guide profile relative to the rail inner side of the rail head and to press it over the entire length of the guide profile, and - the measuring head frame has at least one vertical guide and two vertical linear drives for vertical adjustment of the measuring head with respect to the rail, in order to move the guide profile relative to the rail top side of the rail head and to press it over the entire length of the guide profile.