•Nonlinear static analyses for the seismic assessment of masonry buildings.•Seismic assessment of existing complex masonry buildings with flexible floors.•Vulnerability assessment of mixed masonry–reinforced concrete buildings.•Reliable models and strength criteria for masonry pier and spandrel elements.•An advanced modelling tool useful both at research level and engineering practice. The seismic analysis of masonry buildings requires reliable nonlinear models as effective tools for both design of new buildings and assessment and retrofitting of existing ones. Performance based assessment is now mainly oriented to the use of nonlinear analysis methods, thus their capability to simulate the nonlinear response is crucial, in particular in case of masonry buildings. Among the different modelling strategies proposed in literature, the equivalent frame approach seems particularly attractive since it allows the analysis of complete 3D buildings with a reasonable computational effort, suitable also for practice engineering aims. Moreover, it is also expressly recommended in several national and international codes. Within this context, the paper presents the solutions adopted for the implementation of the equivalent frame model in the TREMURI program for the nonlinear seismic analysis of masonry buildings.