Modern standards for constructions in seismic zones allow the construction of buildings able to dissipate the energy of the seismic input through an appropriate location of cyclic plastic deformations involving the largest possible number of structural elements, forming thus a global collapse mechanisms without failure and instability phenomena both at local and global level. The key instrument for this purpose is the capacity design approach, which requires an appropriate selection of the design forces and an accurate definition of structural details within the plastic hinges zones, prescribing at the same time the oversizing of non-dissipative elements that shall remain in the elastic field during the earthquake. However, the localization of plastic hinges and the development of the global collapse mechanism is strongly influenced by the mechanical properties of materials, which are characterized by an inherent randomness. This variability can alter the final structural behaviour not matching the expected performance. In the present paper, the influence of the variability of material mechanical properties on the structural behaviour of steel and steel/concrete composite buildings is analyzed, evaluating the efficiency of the capacity design approach as proposed by Eurocode 8 and the possibility of introducing an upper limitation to the nominal yielding strength adopted in the design