The main objective of this work is to assess the vulnerability and seismic risk of typical existing modernist unreinforced masonry (URM) modernist buildings and aggregates situated in the Eixample district of Barcelona, part of the architectural heritage of the city. The context of the analysis is the methodology proposed by the Risk-UE project. The buildings are characterized by their capacity spectrum and the earthquake demand is defined by the 5% damped elastic response spectrum, considering deterministic and probabilistic earthquake scenarios. A discussion addresses the basis of the seismic damage states probabilities and the calculated damage index. An important research effort has been focused on the buildings modeling. All the architectural elements and their mechanical properties have been studied and evaluated accurately. It has been evidenced that a detailed and complete knowledge of all the structural elements existing in this type of buildings influence directly their behavior and hence the calculations and the results. The analysis of the isolated buildings and of the aggregate building has been performed for both mentioned seismic scenarios. Finally, a complete discussion of the results is included.