•Seismic failure mechanisms expressed by a single failure mode interaction surface.•Vertical load variation and zero-moment position affecting the lateral strength of URM piers.•Equivalent frame model with N–V failure mode interaction plastic hinges.•Application of the IN2 method for application to URM structures.•Comparison between the IN2 method and IDA for URM. The paper presents a relatively simple and computationally less demanding technique for the modeling and analysis of regular unreinforced masonry (URM) structures. This technique is based on the equivalent frame approach, and incorporates linear beam elements and the plastic hinge concept. The complex seismic failure mechanism of masonry piers is expressed by a single failure mode interaction surface (an “FMI surface”), taking into account the influence of variation in the pier’s vertical loading, and its bending moment distribution. The effect of the governing mechanical and geometrical parameters which determine the shape of the FMI surface is presented and discussed. For modeling purposes, the ultimate lateral strength of a masonry element is expressed as a section which cuts through the FMI surface. A single failure mode interaction plastic hinge (an “FMI hinge”) for each masonry frame element is introduced by combining specific failure modes, taking into account their minimum envelope. Calculations were carried out using the commercially available computer program SAP2000 Ultimate, and the validity of the proposed modeling procedure was confirmed by means of a comparative analysis of an URM wall assemblage which has already been studied by other researchers, using different modeling techniques and analysis software. The effect of the vertical loading acting on piers was studied, as well as the formation of typical failure mechanisms throughout the structure. The final part of the paper broadens the research to a fictitious 3D URM structure, where the out-of-plane behavior of piers has been considered alongside the standard in-plane failure mechanisms. Results obtained using the incremental N2 method were compared, for a range of ground-motion intensities, with selected results obtained using incremental nonlinear dynamic analysis.