The friction force between the contact surfaces of a reactor internal hold-down spring (HDS) and core barrel flanges can directly influence the axial stiffness of an HDS. However, friction coefficient cannot be obtained through theoretical analysis. This study performs a mathematical deduction of the physical model of an HDS. Moreover, a mathematical model of axial load P , displacement δ , and flexibility coefficient is established, and a set of test apparatuses is designed to simulate the preloading process of the HDS. According to the experimental research and theoretical analysis, P -δ curves and the flexibility coefficient λ are obtained in the loading processes of the HDS. The friction coefficient f of the M1000 HDS is further calculated as 0.224. The displacement limit load value (4,638 kN) can be obtained through a displacement limit experiment. With the friction coefficient considered, the theoretical load is 4,271 kN, which is relatively close to the experimental result. Thus, the friction coefficient exerts an influence on the displacement limit load P . The friction coefficient should be considered in the design analysis for HDS.