A method for three-dimensional measurement of coordinates of a set of N predetermined points of the surface of a mechanical part to be measured, relatively to a predetermined reference system, and the direction cosines of the theoretical normals thereto at the theoretical points corresponding to the N predetermined points are known, and including a preparatory phase, in which the coordinate points, corresponding to the N predetermined points of a first mechanical part taken as a standard part, are measured; an initialization phase, in which displacement measurements (along the normals are read on the N points of the standard part; a measurement phase, in which N linear displacement measurements performed on the N points of the part to be measured corresponding to the N points of the standard part, are read; and a computation phase, in which the coordinates of the N points of the part to be measured are computed.