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The physical structure of electrical tree propagation in epoxy resin was studied in a 2-dimensional geometry. Two steps of tree tests have been carried out. In the first step we had been using specimens with and without filler, under humid and dry conditions. As a second step, specimens with several kinds of filler contents under room conditions were used. Then, all of electrical trees propagated were structurally characterized by determining their fractal dimensions. In one sense, it is considered that filler would create such an obstruction to the tree propagation, both in humid and dry conditions. In room condition, the more filler content, the more obstruction is generated, leading to the suppression of tree propagation. In other sense, the introduction of filler brought the rise in fractal dimension due to the increase of branches, both in humid and dry conditions. Also, fractal dimension in dry condition were higher than that in humid condition, for both without and with filler specimens. Furthermore, in room condition, the more filler contents, the higher fractal dimension and damaged area occurred. In this context, the larger fractal dimension and damaged area mean more branching pattern but the characteristics are not necessarily connected with the meaning that a material is easy to destroy when its fractal dimension and damaged area are large.