Previous research in "nite element formulation of #exible mechanisms usually neglected high order terms in the strain-energy function. In particular, the quartic term of the displacement gradient is always neglected due to the common belief that it is not important in the dynamic analysis. In this paper, we show that this physical intuition is not always valid. By retaining all the high order terms in the strain-energy function the equations of motion naturally become non-linear, which can then be solved by the Newmark method. In the low-speed range it is found that the dynamic responses predicted by non-linear and linear approaches indeed make no signi"cant di!erence. However, when the rotation speed increases up to about one-"fth of the fundamental bending natural frequency of the connecting rod, simpli"ed approaches begin to incur noticeable error. Speci"cally, for a connecting rod with a slenderness ratio of 0)01 the conventional simpli"ed approaches overestimate the vibration amplitude almost 10-fold when the rotation speed is comparable to the fundamental natural frequency of the connecting rod. Therefore, non-linear "nite element formulation taking into account the complete non-linear strain is needed in analyzing high-speed #exible mechnisms with slender links.