Studying the stress–strain relationship of fiber-reinforced polymer (FRP)-confined rubber concrete (RuC) plays an important role in its application in engineering projects. Most of the existing stress–strain relationship models are established based on the test data of FRP-confined rubber concrete with circular cross-sections, and the effect of the section shape is not considered. Therefore, an analysis-oriented stress–strain model of FRP-confined circular and square rubber concrete columns was studied in this paper for the first time. A database that includes the rubber particle content and section shape on the peak stress-peak strain and axial–lateral strain relationship of FRP-confined rubber concrete was established by collecting 235 test data from the literature. By modifying the key parameters in the existing FRP-confined normal concrete stress–strain relationship model, a unified stress–strain relationship model of FRP-confined RuC with circular and square columns is established. The proposed model is verified, and a good accuracy of the model is proven.