The upper support form of the flexible support rotor is non-contact magnetic bearing, and the lower is thrust bearing. Therefore, the lower support is the only dynamic-static contact component of the flexible supported rotor. The axial bearing capacity of the lower bearing has direct influence on the stability of the rotor. To study the mechanism of bearing capacity influencing rotor is an important prerequisite for bearing design and optimization. A non-rigid connection model of the lower support was established and introduced into the rotor model to study the influence of bearing capacity on rotor stability. The dynamic response of the rotor under different bearing capacity was studied theoretically and the stability of the rotor was analyzed. The results show that too small bearing capacity may lead to rotor instability. The results can provide a theoretical basis for the selection of bearing capacity of flexible supported rotor.