Superconducting Conductor on Round Core (CORC®) cables with scalability, flexibility, strong mechanical strength and high current density have become practical conductors in high-field magnets for fusion machines and particle accelerators. However, when it works in a high background magnetic field, the high mechanical stresses that generated in the CORC® conductor can result in irreversible degradation of the conductor. This paper presents the study on mechanical properties of CORC cables. Firstly, a 60cm-long CORC® short sample is fabricated, and its fundamental parameters are measured by experiments, including self-field critical current. Then, the effect of two typical mechanical stresses including longitudinal tensile stress, transverse compressive stress on the critical current of CORC cables has been investigated, respectively. And discussions are carried out by numerical modeling based on multi-physics finite element method. Conclusion obtained in this paper can not only verify the feasibility of CORC cables application in high magnetic field, but also provide valuable guidance in application limit of CORC cables.