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This paper develops a new method for analyzing the structural seismic behavior of single-layer reticulated shells based on exponential strain energy density (ESED). The ESED method reveals a characteristic point from a relationship between ESED sum and peak seismic acceleration. Then, the characteristic point leads to an updated concept of structural failure and an ESED-based criterion for predicting structural failure load. Subsequently, the ESED-based criterion and the characteristic point are verified through numerical analysis of typical single-layer reticulated shells with different configurations and a shaking table test of the scale shell model. Finally, discussions further verify the rationality and application of the ESED-based criterion. The ESED method might open a new way of structural analysis and the ESED-based criterion might indicate a prospect for a unified criterion for predicting seismic failure loads of various structures.