Abstract: Based on experimental data from 122 complete uniaxial tensile stress-strain curves of concrete with three strength grades (C25, C30, and C50), and in conjunction with the tensile constitutive damage model recommended in the Code for Design of Concrete Structures (GB 50010-2010), four key parameters—elastic modulus, tensile peak strength, tensile peak strain, and the concrete descending branch parameter—are identified through an inverse method integrating optimal square approximation with a genetic algorithm. The optimal marginal probability distribution of each parameter is determined using the maximum likelihood estimation, the Kolmogorov-Smirnov (K-S) test, and the Akaike Information Criterion (AIC). Subsequently, a regular vine (R-Vine) Copula model is adopted to characterize the complex nonlinear dependence structure among the four parameters, and its goodness of fit is tested. Conditional sampling techniques are utilized to generate parameter samples with the target correlation structure, thereby reconstructing the stochastic tensile constitutive relationship of concrete that accounts for correlations among constitutive parameters. The research results show that the parameter samples generated via Copula theory reconstruct the tensile constitutive relationship of concrete, and that the statistical characteristics (mean and standard deviation) of the sample curve set closely match those of the parameter-identified curves. A joint probability model for the concrete tensile constitutive parameters across different strength grades is established, extending the concrete parameter correlation analysis from the case of a single strength grade and compressive loadings to multiple strength grades and tensile loadings, which provides a theoretical support for stochastic nonlinear analyses and for the reliability-based design of concrete structures.