In the engineering of large-span space structures, high-rise buildings and bridges, the flexible restraint or tilt of the end of the seismic isolation rubber bearing has a significant effect on its mechanical properties and stability. Based on the theory that the two ends of the bearing have arbitrary turning angle and relative displacement, and combined with the test results under the solid end constraint condition for nonlinear response analysis. It is found that the theoretical solution and the test results are highly consistent with the horizontal displacement of the bearing in a specific state. Following that, the mechanical properties of the bearing under the most unfavourable boundary conditions are further explored by comparing the bearing under four boundary conditions. The analyses show that the top moment of the bearing changes from anti-tilting to tilting moment with the increase of the top turning angle. In addition, the bearing P-Δ effect is that the critical angle of bearing overturning increases with the increase of axial pressure. However, both the increase of top angle and axial pressure will lead to the increase of internal force, deformation and decrease of horizontal stiffness of the bearing, especially the significant increase of the bottom bending moment, which will easily cause the local rupture of rubber inside the bearing, thus leading to the instability of the bearing as a whole.