In this paper, the Concrete Damaged Plastic (CDP) model in the commercial Finite Element software ABAQUS is proposed. The main goal is to capture the stress–strain relationship in both compressive and tensile behavior. In the CDP model, determining damage variables is one of the important issues and needs to be considered. Instead of relying on values from previous studies, the damage variants in compression ( \(d_{c}\) ) and tension ( \(d_{t}\) ) are proposed and expressed by hyperbolic tangent functions. Particularly, the damage variables are adjusted by examine the coefficients \(\alpha\) in compression and \(\beta\) in tension behaviors that most closely match the experiment. To demonstrate the reliability and effectiveness of the proposed model, numerical simulations are performed. Specifically, numerical simulations of high-strength concrete C60, C80, and C110 are conducted. A comparison is made between the simulation of the developed model and experimental data to evaluate the performance of the model. Additionally, to boost the model’s dependability, the paper includes two more instances of reinforced concrete slabs and axially compressed CFT columns. Consequently, the experiment findings and the simulation results derived from the examples show a reasonable degree of consistency. It is demonstrated that the CDP model presented in this research is extremely dependable and can be applied to the simulation of intricate concrete structures.