This paper considers off-line identification of spatial and temporal characteristics of a dynamic load, and is focused on the case of a limited number of sensors. Both elastic and elasto-plastic structural behaviours are taken into account. The identification is performed off-line, based on optimisation of modelled local structural responses, and—in the case of limited number of sensors—identifies an observationally equivalent load, which in a given sense optimally approximates the actual load. Compared to previous researches this approach allows to identify general dynamic loads of unknown locations, including multiple impacts and moving loads, and gives more insight into the identification process by distinguishing between the reconstructible and unreconstructible load components. Additionally, the problem of optimum sensor location is discussed.