To solve the out-of-plane stability problem of the telescopic boom subjected follower forces, the deflection differential equations of the multi-telescopic boom model which under actions of pull-rope are established. With proper boundary conditions, the recurrence formulas of buckling characteristic equations are presented, and the explicit expressions of the boom in some practical applications are given. The influence on destabilizing critical force of telescopic boom due to the ratio of a／l is discussed in detail, where a is the length of wire projected to telescopic boom, and l is the length of telescopic boom. In comparison with the ANSYS method, the results show that the buckling characteristic equations are completely correct. As the ratio of a／l increases, the capacity of anti buckling reduces and tends to be a constant value.