To address the defects of ambiguous physical meaning of empirical parameters and numerical singularity induced by zero denominator in the traditional Duncan-Chang hyperbolic constitutive model, the saturation shell regularization idea from computational mechanics is introduced into geotechnical constitutive modeling in this paper. A single-channel attenuation shell based on the hyperbolic tangent function [1-tanh] is constructed to restrict the tangent modulus strictly between the initial modulus E0 and residual modulus Eres. The characteristic strain εy controlling modulus attenuation can be analytically solved directly from ultimate strength rather than treated as a fitting parameter. Verification is performed using multi-confining-pressure triaxial test data of classic dense sand. The results indicate that the proposed model only requires two effective parameters to achieve comparable precision with the traditional model, and an explicit analytical solution of ultimate strength is derived to completely eliminate the risk of numerical divergence. This novel model provides a singularity-free and physically parameterized approach for describing soil nonlinear mechanical behavior, which is especially applicable to implicit numerical calculation requiring high numerical stability.