The main topic treated in the First Day and the Second Day of Galileo’s Dialogues is the resistance that solids offer to fracture with special consideration to prisms and cylinders submitted to axial tensile loading or to “transverse”, i. e. bending, forces. Although no consideration is given to deformation of the solid before fracture one may say that Galileo implicitly introduces the concept of a Continuum within which coherence forces do act in order to maintain the filaments, fibres or any other constituent particles together. Thus, he opens the way to the concept of stress, which was settled explicitly some 200 years later. Having recognised that coherence forces and gravity forces in a solid are not related in the same way to its geometric scale, he performs what can be considered as the first striking example of dimensional analysis with application to similarity. In its celebrated analysis of the resistance of a cantilever beam submitted to bending, Galileo gives a first attempt to deriving the resistance of a whole solid submitted to some kind of loading from the resistance of its constituent material determined from another test. Together with Coulomb’s celebrated Essay these are two milestones of the Theory of yield design, the fundamental root of Ultimate Limit State Design, which is presently introduced in international codes for civil engineering