The shimmy of the front landing gear of an aircraft usually occurs in the process of taking off or landing, which endangers the stability and maneuverability of the aircraft and is a serious aircraft fault. In this paper, based on the theorem of moment of momentum, a mathematical model of shimmy considering landing gear side bending and torsion is established for a certain type of UAV. The different dynamic models when using traditional oil damping damper and electromagnetic damping damper are discussed. For the traditional oil damping damper, the equivalent linear model is used to obtain the upper and lower boundaries of the critical stability damping curve. For the nonlinear model of electromagnetic damping damper, the bifurcation analysis theory is used to determine the shimmy stability area. It is shown that excessive shimmy damping can not suppress shimmy, and the stable region of shimmy on the parameter plane is obtained, It can provide some references for the design of landing gear shimmy reduction.