The general practice in structural assessment or design using 3D seismic analysis of inelastic structures is to obtain the responses (such as storey displacement, inter-storey drift, etc.) by applying the bidirectional components along any arbitrarily chosen structural axes. However, such response quantities may not remain the same when the bidirectional components are rotated with respect to the structural axes. It becomes relevant to identify the angle of seismic loading which maximizes the response quantity in the structure, and that angle would be called as critical angle of incidence (CAI), and the associated response as critical response. Nevertheless, a single CAI which can simultaneously maximize all the responses of the structure does not exist, rather the critical angle varies according to the type of response and earthquake loading. Therefore, any structural assessment or design of buildings based on the responses obtained from applying the earthquake loading along user defined structural axes may not be always conservative. To avoid such scenarios the critical responses should be estimated considering the effect of angle of seismic incidence. To address such an issue, pertaining to inelastic structures, this study presents a new approach which essentially combines bidirectional pushover analysis with an already existing non-linear static procedure called the Extended-N2 method. © 2021, The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.