It is of great importance for enginsering applications to obtain the expression of scattering field for an ellipsoidal target irradiated by an electromagnetic wave from an arbitrary direction.Literature relevant to this problem is seldom found.In this paper,the scattering field for an ellipsoidal target is presented by utilizing the scale transformation of electromagnetic field and the rotation of coordinate system,with an electromagnetic wave projecting on the target from an arbitrary direction.The obtained result is in good agreement with the solution available from the literature if we consider the scale factors to be unity.Taking a conducting ellipsoidal target for sample,we perform the partial simulations of the ellipsoidat model and a plant leaf model by choosing different scale factors.The obtained results show that the distribution characteristic of scattering field is sensitively affected by the polarization of the incident wave and varies not much with the incident wave angle but changes with the observation point.At some points the scattering energy arrives at its maximum.