An apparatus measures displacement of a structure having a curved surface, such as a pipe, conduit, shaft or rod. The apparatus includes a support structure having opposing first and second ends, with a first laser distance measurement device at the first end and a second laser distance measurement device at the second end. The laser distance measurement devices generate dual laser beams that illuminate the curved surface of the structure, detect laser energy reflected from the curved surface of the structure, and generate distance signals based on the detected laser energy. A measurement device on the support structure measures a spacing between the two laser beams. The support structure is pivotally attached to a stabilizing base, thereby providing for the tilting of the support structure and the laser beams. An inclinometer on the support structure measures an angle of tilt. A computer processor calculates position values indicating displacement of the curved surface based on the distance signals, the spacing between the laser beams, the radius of curvature of the curved surface, and the angle of tilt of the laser beams. Tripod-mounted and portable handheld versions of the apparatus are described.