The constitutive model is essential for predicting the deformation and stability of rock-soil mass. The estimation of constitutive model parameters is a necessary and important task for the reliable characterization of mechanical behaviors. However, constitutive model parameters cannot be evaluated accurately with a limited amount of test data, resulting in uncertainty in the prediction of stress-strain curves. This paper proposes a Bayesian analysis framework to address this issue. It combines the Bayesian updating with the structural reliability and adaptive conditional sampling methods to assess the equation parameter of constitutive models. Based on the triaxial and ring shear tests on shear zone soils from the Huangtupo landslide, a statistical damage constitutive model and a critical state hypoplastic constitutive model were used to demonstrate the effectiveness of the proposed framework. Moreover, the parameter uncertainty effects of the damage constitutive model on landslide stability were investigated. Results show that reasonable assessments of the constitutive model parameter can be well realized. The variability of stress-strain curves is strongly related to the model prediction performance. The estimation uncertainty of constitutive model parameters should not be ignored for the landslide stability calculation. Our study provides a reference for uncertainty analysis and parameter assessment of the constitutive model.