In order to study the effect of elastic support stiffness on the stability performance of rectangular steel tube concrete flange I-shaped beams, stability performance tests were conducted on three rectangular steel tube concrete flange I-shaped beams with different elastic support stiffnesses under concentrated load. The displacement and strain changes of the test beams were studied, and the instability form and stable bearing capacity of the beams were obtained. The experimental results show that the entire loading failure process is divided into three stages, namely the elastic stage, the elastic-plastic stage, and the failure stage. All three test beams experience overall bending torsional buckling instability. As the stiffness of the elastic support increases, the stable bearing capacity of the beam increases, which verifies that setting elastic support can effectively improve the stable bearing capacity of the beam. On the basis of the experimental results, nonlinear buckling analysis was conducted on the beam using ANSYS finite element software. The obtained stable bearing capacity is compared with the experimental results, and the error is less than 5%, thus verifying the correctness of the finite element analysis method. Finally, the influences of parameters such as concrete strength, upper flange steel content, and web thickness ratio on the stability performance of this type of beam are studied. The results show that increasing the steel content of the upper flange steel pipe and reducing the height to thickness ratio of the web can significantly improve the stable bearing capacity of the beam, while enhancing the concrete strength has a relatively small effect on the stable bearing capacity of the beam.