This paper discusses the significance of a new tool, the Inertia Moment Projection (IMP) ellipsoid (or ellipse in two dimensions), for the deformation description and strain analysis of structural objects with arbitrary shape. During the progressive uniform deformation, the deformation of the IMP ellipsoid is coincident with that of the structural object. They both follow the same deformation rule. The IMP ellipsoid is equivalent to the arbitrary shape of structural object for the description and analysis of deformation. It has the same characteristics as the finite strain ellipsoid and can substitute for the structural object for strain analysis. So, the former strain analysis methods based on elliptic structural deformation markers can be used for the general structural objects with arbitrary shape. It would be a very useful mathematic tool for the description and analysis of structural deformation.