A tracking device is provided with a non-contact type displacement gauge, a positioner which moves a flaw detecting sensor within a plane perpendicular to an axial direction of a pipe or tube, and a positioning controller which controls the positioner. The positioning controller predicts a time until a portion of the pipe or tube whose displacement is measured by the displacement gauge reaches a predetermined position on a straight line extending in a Z-axis direction through a rotational center of the pipe or tube on the basis of the positional relationship between the displacement gauge and the flaw detecting sensor and a rotational speed of the pipe or tube; controls the positioner on the basis of the displacement measured by the displacement gauge and an operational delay time of the positioner in such a manner that the relative position of the flaw detecting sensor to the pipe or tube after the lapse of the predicted time becomes substantially constant in the Z-axis direction; and moves the flaw detecting sensor along the Z-axis direction. The positioning controller performs the same control in an X-axis direction.