The definition of the seismic demand and the correct characterization of the mechanical properties of the materials are two of the major difficulties in the seismic damage assessment of unreinforced masonry buildings due to the large uncertainties and variability that they present. A seven-story unreinforced masonry building in Barcelona, Spain, is taken as a case-study and modeled as an isolated solid clay structure with unidirectional iron beams-brick vaults slabs and load-bearing walls. In order to overcome the material definition shortcomings, the compressive strength, Young modulus, shear modulus and shear strength are modeled as random variables. On the other hand, the seismic demand variability is addressed through a set of different ground motions selected with the conditional spectrum method and subsequently scaled to different levels of demand (pga) as the incremental dynamic analysis methodology suggests. Due to computational and time limitations, a sufficiently representative sample is selected firstly from the population of mechanical properties, and secondly from the population of dynamics analyses for each direction of analysis. The obtained results show the correlation and different grades of influence for each of the selected random variables and levels of seismic demand (pga).