The elastic redundancy is defined first, which is different from the conventional geometrical redundancy. Because the elastic redundancy of the pinjointed bar structures is dependent not only on the elastic stiffness but also on the geometry topology. The governing equations of equilibrium equation, physical equation and geometric equation are formulated from differential of the potential energy equation. After linearizing the geometry equation, and substituting it into the other two equations, the elastic redundancy formula is yielded. The presented algorithm is implemented with matlab. The benchmark examples unveil the characteristics of the elastic redundancy of the pin-jointed bar structures.