Obtaining scattering field for an ellipsoid irradiated by electromagnetic wave with arbitrary polarizing and propagating direction is a hard topic that has caused large attention in the world. Literatures relative to it are seldom found. In this paper, the scattering field for an ellipsoid is presented by utilizing the scales transformation of electromagnetic field and coordinate system rotation, as the incident wave irradiating the target with arbitrary polarizing and propagating direction. The result obtained is in good agreement with that in the reference when all the scale factors changes into 1. We take a conductor ellipsoid as an example, simulations both for ellipsoid and plant leaf are presented respectively by way of choosing the different scale factor. Results show that the scattering field is sensitively affected by polarization of the incident wave and varies not too greatly with the incident wave and changes with the observing point. At some points the scattering energy arrives to its maximum.
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