In earthquake engineering, acceleration has played a major role, while wave energy has rarely been considered as a demand in design. In order to understand earthquake damage mechanism in terms of energy, the demand in terms of wave energy in surface soil layers is studied here, assuming one-dimensional SH wave propagation by using a number of vertical array records during nine strong earthquakes in Japan. A clear decreasing trend of the energy demand with decreasing ground depth and decreasing surface soil stiffness has been found as well as a propensity of incident energies calculated at bedrocks being roughly compatible with empirical formulas. How the energy demand is correlated with structural damage is also discussed in simplified models to show that induced structural strain is governed by upward energy flux, degree of structural resonance, and impedance ratio between structure and ground and structural stiffness. In low-damping brittle superstructures, wave energy flux in resonance and associated predominant frequency are decisive in determining the damage, while cumulative wave energy determines the damage in high damping ductile soil and massive concrete structures. The trend of lower energy demand in softer soil sites may not be contradictory, with a widely accepted perception that softer soil sites tend to suffer heavier earthquake damage as far as geotechnical damage is concerned.