In order to investigate the effect of inorganic dielectric fine particle mixed in Low Density Polyethylene on the deterioration by treeing, a comparative study for initiation and development of the tree has been carried out between the pure thin film specimen and the same geometrical specimen mixed with a constant weight percent by a defiend particle size of $Al_{2}$O$_{3}$ and SiO$_{2}$, having larger dielectric constants than that of the base material. According to the results, it has been observed that as increasing dielectric constant, the initiation of tree is expedited, however, the development of the tree reached at the surface of filler particles shows the suppressive trends. From these facts, a reasonable interpretation may be possible by considering the effect of intensified electrical field around the tip in the presence of filler particles, that the initiation and the development of tree are a mechanical break down process caused by Maxwell stress due to the concentration of electrical field at the tip. This suppressive effect is specifically suggestive for the reason that a discharge route must be constructed around the particle surface because of the intensified field strength near filler, which, in turn, reduces the geometrical curvature of the tip so that the local intensity of electrical field can be relaxed. Further more an experimental evidence for this assumption was able to observe in this investigation.