To study the stability performance of rectangular tubular flange composite beams with torsional bracing set at the mid-span under concentrated loads, the "plate-beam theory" was adopted, and the elastic lateral-torsional buckling total potential energy equation of the rectangular tubular flange composite beam was established. The displacement functions were selected, and the energy variation method was used to solve the buckling equation, and the analytical solution for the elastic lateral-torsional buckling critical moment of the rectangular tubular flange composite beam was obtained. Then, using the 1stOpt soft ware, considering the influence of multiple parameters, the elastic critical moments of the composite beams under different cross-sectional dimensions, spans, and torsional bracing stiffness were fitted, and the calculation formulas for the elastic critical moments of the composite beams with and without torsional bracing were obtained. These formulas were compared with the finite element analysis results, and the error was within 5%, verifying the accuracy of the calculation formulas. Finally, the influence laws of parameters such as concrete strength, web height-thickness ratio, span-height ratio, and upper flange steel content ratio on the stability performance of the rectangular tubular flange composite beam were analyzed. The study found that as the torsional bracing stiffness increased, the elastic lateral-torsional buckling critical moment of the composite beam gradually increased, and the stability of the beam was improved; when the torsional bracing stiffness reached the threshold stiffness, the elastic lateral-torsional buckling critical moment of the composite beam no longer increased; changing the concrete strength or web height-thickness ratio would not cause significant changes in the elastic lateral-torsional buckling critical moment of the beam, while reducing the span-height ratio or increasing the upper flange steel content ratio would significantly increase the elastic lateral-torsional buckling critical moment of this type of composite beam.