Abstract Various aspects of the forced response of a damped one-dimensional periodic structure are considered. Initially, the attenuation produced by damping is investigated, and it is shown that this may be of the same order of magnitude as the localization factor produced by structural irregularity. An efficient approximate method for predicting the energy level in each bay of a forced periodic structure is then presented. This method is based on vibrational energy flow, and excellent agreement with exact results is demonstrated for a periodic beam system. The effect of damping on the response is investigated and it is found that the benefits which would normally be expected from an increase in damping can be offset to some extent by an increase in vibration localization (or concentration near the excitation point) arising from the attenuation factor. It is also found that a decrease in the pass band width leads to an increase in response for both harmonic and broadband random loading.