Concrete, as a complex and anisotropic material, poses challenges in accurately simulating its behavior in numerical simulations. This paper focuses on selecting an appropriate constitutive model for simulating the behavior of a steel–concrete composite column using finite element analysis under compression and push-out tests. Two models are analyzed and compared, namely, Drucker–Prager and concrete damage plasticity. The results demonstrate that the concrete damage plasticity model outperforms the Drucker–Prager model in all six test cases, indicating its superior accuracy in capturing the composite column’s behavior. This study enhances the reliability of numerical simulations for steel–concrete composite structures by choosing the most suitable constitutive model, parallel with extensive sensitivity analysis and model calibration. The findings emphasize the significance of meticulous model selection and precise parameter definition for achieving accurate predictions of concrete behavior. This research contributes to advancing the understanding and modeling of concrete’s intricate behavior in structural analyses.