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Recently the backscattering of an electromagnetic (EM) missile with an energy decreasing as r-ϵ by a perfectly conducting plate has been studied and the analysis shows that the energy backscattered varies as r-ϵ with the same exponent as the incident EM missile. Scattering of an EM missile by other shapes is left as an open question. In this paper we study the backscattering of an EM missile with energy decreasing as r-ϵ by a perfectly conducting elliptical cylinder. It has been shown that the rate of the energy decay for the backscattered field far from the cylinder is proportional to r-(1+ϵ), which is faster than r-ϵ for plate scattering but still slower than the ordinary energy decay r-2 for a two‐dimensional backscattered field.