Abstract: Traditional studies on earthquake input energy spectra are based on the theory of single degree of freedom system (SDOF) subjected to single directional earthquake excitations, in which the multi-dimensionality of earthquake excitations and the coupling of non-linear structural responses are not considered. In this study, a single-mass dual-degree of freedom system subjected to bi-directional earthquake excitations is proposed. The two-dimensional yield surface elasto-plasticity theory is enforced. The standard earthquake input energy spectrum under bi-directional earthquake excitations is presented. The statistical average spectra are established based on strong earthquake motion records for hard, medium and soft soil sites, respectively. The influences of the soil site, ductility factor and the period ratio on average spectra are analyzed. Results indicate that standard earthquake input energy spectra for each soil site show different characteristics. The influences of the ductility factor on spectra are obvious in hard and medium soil sites, but are not as significante in soft soil sites, excluding with long periods. The period ratio is also found to impose centain effects on the spectra. In some instances, the earthquake input energy responses are found to be overestimated when the SDOF system is adopted.