Analytical and experiment study on vibratory tillage tools by adding an external energy to the tillage tools has been widely applied. This method would significantly reduce soil's resistance; unfortunately it uses a lot of energy. Self excited vibration phenomenon on vibrating subsoiler has also been shown experimentally reduce soil's resistance though not as much as the former. However no analytical study of the latter method can be found. This paper present mathematical derivation of shank-subsoiler's vibration due to natural excitation of varied cutting forces. Shank-subsoiler was modeled as a single degree of freedom; while the natural excitation of varied cutting force was modeled as a periodic function. This paper also discusses the effect of spring's elasticity to maximum displacement of the tillage-tools. Therefore, the possibility of decreasing the soil-cutting force for loosening soil's density due to self exited vibration significantly is visualized