A new way of energy storage based on mechanical elasticity is proposed. Nonlinear dynamic model of permanent magnet motor based mechanical elastic energy storage unit is derived, and the chaotic behaviors under certain parameter values and operation conditions are demonstrated. The linear stability of the nonlinear dynamic model is analyzed. Based on the operation parameters of the 0.16 kWh/0.8 kW unit that is being developed in our laboratory, three-dimensional nonlinear model is reduced to two-dimensional projection subsystem with varying parameters. Then the chaotic property of the unit is analyzed by coordinate plane projection method, the changing relationship between the locations of equilibrium point, characteristic equation of reduction subsystem and varying parameters is discussed, and the chaotic behavior is numerically verified. The issue caused by poor applicability of analytical methods and solved only by simulation is solved to some extent at a theoretical analysis level.