Abstract: As for the state of zero deflection of clamp-clamp Eulerbeam acted on uniform distributed couple only, the inherent factors toinduce this zero deflection can be analyzed by forth order differentialequation of deflection of Euler beam that take into the effect ofdistributed force and couple. Then Euler beam acted on uniform distributedcouple with the six kinds of classic boundary condition has been analyzed.The key factor inducing the zero deflection of Euler beam acted on uniformdistributed couple only can be found is whether shear force in boundarycondition equal to zero.