Abstract Most of the model updating techniques do not employ damping matrices and hence cannot be used for the accurate prediction of complex frequency response functions (FRFs) and complex mode shapes. In this paper, the response function method (RFM) is extended to deal with the complexity of FRF and modal data using complex updating parameters. In the proposed model updating procedure, the finite element model is updated in such a way that the updated model reflects general damping in the experimental model by considering the updating parameters as complex. The effectiveness of the proposed finite element updating procedure is demonstrated by numerical examples as well as by actual laboratory experiments. First, a study is performed using numerical simulation based on a fixed–fixed beam structure with structural damping, viscous damping and structural and viscous damping models. Various levels of damping and noise are assumed in the data. The numerical study is followed by a case involving actual measured data for the case of an F-shaped test structure. The updated results have shown that the complex updating finite element model updating procedure can be used to derive an accurate model of the system. This is illustrated by matching of the complex FRFs obtained from the updated model with that of experimental data.