Abstract: A concreting rig for use in construction by the cantilever method of an elevated, elongated civil engineering work, such as a bridge, elevated road, roof or the like, by in situ concreting longitudinally consecutive sections of the work with the rig overhanging beyond the already completed portion of the work, comprises a rigid structural frame which is longitudinally pressed against the already completed portion of the work, by means of tensioned prestressing members. The rig bears on the already completed work portion by way of at least three abutment devices each of which engages with a complementarily-shaped locating print in the completed work portion, means being provided for predetermining the position of each locating print in dependence upon the geometric characteristics of the work and the position therein, of the section to be concreted.