•2D and 3D nonlinear pushover and incremental dynamic analyses (IDA) were performed.•Using OpenSees the behavior of a 4-story modular steel building (MSB) was evaluated.•Diaphragm interactions, relative displacements and rotations of modules were studied.•The force transfer through connections and column discontinuities are considered. Modular steel construction is a relatively new construction technique that considerably reduces the time spent on the construction site. However, due to the detailing and assembly requirements of multi-story modular steel buildings (MSBs), these systems are prone to undesirable failure mechanisms during large earthquakes. In this paper a 4-story MSB is designed considering realistic constraints posed during the modular construction. Using a detailed model in OpenSees an assessment of the seismic demand and capacity of this MSB is provided by performing nonlinear static pushover and incremental dynamic analyses (IDA) in two and three dimensions. Diaphragm interactions, relative displacements and rotations between modules, the force transfer through horizontal connections, column discontinuity coupled with possible high inelasticity concentration in vertical connections are some other important aspects that are specifically considered. The results that are summarized with relevant conclusions provide a better insight to the dynamic behavior of multi-story MSBs.