Landing gear is a structure that is mounted under the fuselage and helps the aircraft in takeoffs and landings. The most important duty of landing gear is the control of vibration exerted on the system through the shock absorber which is a common component to all the landing gear. Considering the importance of this issue, the necessity of investigating shock absorber with features such as high efficiency, reliability and maintenance, etc. is undeniable. In the present study In addition to choosing hydro pneumatic shock absorber its relationships arising from oil and gas liquids have been studied. This research was conducted with the aim of reducing the force variations and vibrations, with a focus on liquid gas. Thus, according to the gas laws, initially gas flow in the case of practical modes of isotherms during the taxi and poly trophic during landing has been studied. Considering that in the shock absorber only one mode can be used and Isotherms mode despite less vibration is not responsible for the landing phase and poly trophic mode exerts a lot of vibration on the fuselage, therefore a situation that can meet both needs in a way that have both phases of taxing and landing and at the same time reducing vibrations to be followed is the combination mode that its relation has been extracted at the end. The results of the extracted relations using numerical methods compared with practical results shows that not only the force on the aircraft body but also the vibrations on it have been significantly reduced and improves system performance. Manuscript profile