During modal testing, the test structure is connected to its surroundings by a suspension system. Cable suspension system is one of the most common suspension systems which is used to simulate the free-free condition, due to its low stiffness. In this condition, the measured modal properties are assumed to be free-free dynamic properties of the test structure. But in situations in which the test structure is big and flexible, the stiffness of the suspension system is comparable with the stiffness of the test structure and cannot be neglected. In this paper, the suspension effects are eliminated from measured modal frequencies of a flexible structure which is suspended by a cable suspension system. The eigenvalue sensitivity analysis is done and then, the effective stiffness of the cable suspension system is derived. Based on the eigenvalue sensitivity and the effective stiffness of the suspension system, an iterative procedure is proposed to eliminate the suspension effects from measured modal frequencies of the test structure. The proposed iterative procedure is verified using a finite element model. Finally, the proposed iterative procedure is used to eliminate the suspension effects from measured modal frequencies of a real flexible structure.