Constitutive model of stone masonry is an important foundation and prerequisite for physical calculation and finite element numerical simulation of stone masonry. In order to further study the constitutive relationship of stone masonry under uniaxial compression, based on the theory of damage mechanics, the two-parameter Weibull distribution function was applied to reflect the damage variable, and its parameters were determined according to the characteristic conditions of the whole process of the stress-strain curve of stone masonry under uniaxial compression. The uniaxial compression damage constitutive model of stone masonry was derived and established, and the correctness of the constitutive model was verified by the existing test data. The constitutive model was compared with the typical masonry constitutive model. Finally, the finite element analysis of the existing stone masonry arch bridge test was carried out to verify the applicability of the constitutive model. The results show that the model is in good agreement with the uniaxial compression test results of existing stone masonry. The established model verifies the general law of masonry damage evolution and accords with the general trend of typical masonry constitutive model. The model can be applied to the finite element analysis and calculation of masonry structure with good applicability.