A method and apparatus for measuring a surface using a surface sensing device mounted on a scanning head on a member of a coordinate positioning apparatus. The coordinate positioning apparatus may be operated to produce relative movement between the scanning head and the surface profile and the scanning head includes a drive for producing rotational movement of the surface sensing probe about one or more axis. A desired measurement profile on the surface which the surface sensing device will track and the desired motion of the orientation of the surface sensing device as the surface' sensing device follows the measurement profile are defined. This data is used to derive the required path of the relative motion between the member of the coordinate positioning apparatus and the surface, such that the surface sensing device prescribes a trajectory along the measurement profile.