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A time domain (TD) analytical analysis of electromagnetic (EM) transient scattering from a perfectly conducting ellipsoidal-like surface with a finite edge contour is performed by using an approximation of TD physical optics (TD-PO). In particular, a closed-form solution has been developed in the case when the surface is illuminated by a transient-step plane wave. An ellipsoidal surface is selected in this study because it may resemble a variety of realistic surfaces such as spherical, parabolic or planar surfaces. The integration of these various finite ellipsoidal-like surfaces may be used to model a realistic scattering object such as an aircraft, which makes this solution very applicable to treat realistic problems in an effective fashion.