Abstract: Based on the nonlinear magnetic-elasticity kinetic equations, physicalequations, electrical kinetic equations and the expression of Lorentz force,a nonlinear dynamic model of Euler pole is established by using theLagrangian description method. After the simplifications of the nonlineardynamic model, the bifurcations of a nonlinear static model, a lineardynamic model and a simplified nonlinear dynamic model with a cubic nonlinearitem are analyzed, respectively. As an example, the curves of the critical buckling load vs. related the relative parameters are obtainedwhen a pole is applied with compressive force in a magnetic field. Thecalculated results are discussed.