Bidirectional energy-based pushover (BEP) procedure is expanded in this paper to predict approximate incremental dynamic analysis (IDA) results of medium- and high-rise structures. BEP is a unique approach in the sense that it provides approximate IDA curves under the simultaneous effect of two horizontal components of ground motions and is applicable to both symmetric- and asymmetric-plan buildings. The method has already proved to be useful in low-rise buildings, and this study aims to evaluate its suitability for mid- and high-rise structures. Six structural models were considered in this evaluation in two groups of 9- and 20-story buildings, with each group consisting of a symmetric, a one-way asymmetric, and a two-way asymmetric-plan building. The results revealed that the method was sufficiently accurate to provide approximate IDA curves for all structural models. The method had similar accuracy in the asymmetric models as it did in the symmetric models, although the accuracy slightly decreased as the height of the building increased. BEP also provided good estimates of the demands in both ‘flexible’ and ‘stiff sides’ of the asymmetric buildings as well as the demands over the height of the buildings.