The ATLAS forward, or endcap, muon spectrometer covers the rapidity region of 1:0ojZjo2:8 and extends over a volume of approximately two times 5000 m 3 . High-precision muon tracking chambers are used to measure track sagittas with 50 mm accuracy. An optical alignment system will monitor the relative spatial positions of these chambers with an accuracy of 30 mm, such that the contribution of the chamber location to the global sagitta error remains below 40 mm. The alignment concept relies on devices called alignment bars; these are long tubes (up to 9:6 m) whose shape is constantly monitored at the level of 20 mm by internal alignment sensors, and on which further alignment sensors are mounted in order to determine the positions of the nearby chambers. In order to derive the shape of an alignment bar from the readings of the internal sensors monitoring it, a model to describe deformations and a calibration procedure are required. This paper describes the design of the alignment bars, the method for reconstructing the shape from the sensor readings, and the calibration of an alignment bar on a large coordinate-measurement machine. The performance of a single bar, and the performance of an ensemble of bars in a large-scale test environment are discussed.