In the first part of the paper the author gives a short description of the possibilities of testing on real structures and then on models of them (using computers or physical tools). Details about the application of physical models in static and dynamic fields are also provided. Tests carried out, with the aid of several physical models, on the large columns supporting the tiburium of the Duomo of Milan are presented. Some indications about the reconstruction of these columns and the monitoring applied for the automatic measurement of the displacements and strains are given in conclusion.