A 54-story steel, perimeter-frame building in downtown Los Angeles, California, is identified by a wave method using records of the Northridge earthquake of 1994 (ML = 6.4, R = 32 km). The building is represented as a layered shear beam and a torsional shaft, characterized by the corresponding velocities of vertically propagating waves through the structure. The previously introduced waveform inversion algorithm is applied, which fits in the least squares sense pulses in low-pass filtered impulse response functions computed at different stories. This paper demonstrates that layered shear beam and torsional shaft models are valid for this building, within bands that include the first five modes of vibration for each of the North–South (NS), East–West (EW), and torsional responses (0–1.7 Hz for NS and EW, and 0–3.5 Hz for the torsional response). The observed pulse travel time from ground floor to penthouse level is τ ≈1.5 s for NS and EW and τ ≈ 0.9 s for the torsional responses. The identified equivalent uniform shear beam wave velocities are βeq ≈ 140 m/s for NS and EW responses, and 260 m/s for torsion, and the apparent Q ≈ 25 for the NS and torsional, and ≈14 for the EW response. Across the layers, the wave velocity varied 90–170 m/s for the NS, 80–180 m/s for the EW, and 170–350 m/s for the torsional responses. The identification method is intended for use in structural health monitoring. Copyright © 2013 John Wiley & Sons, Ltd.