To study the influence of masonry methods on the mechanical properties of ordinary brick masonry walls, based on existing experimental data, a quintic polynomial mathematical model is used, the method is determined with reference to the concrete constitutive model relationship, and a masonry method influence coefficient is introduced to comprehensively describe the entire process of constitutive relationship curves for three different masonry methods. Separate modeling of ordinary brick masonry specimens is conducted by means of the finite element software ABAQUS and the numerical simulation results and the experimental data are compared to analyze the stress-strain curves, ultimate bearing capacity, and compressive strain; and a compressive constitutive model for masonry structures incorporating the masonry method influence coefficient is subsequently derived. After the accuracy of the constitutive model was verified, it can meet the engineering calculation requirements and improve the precision of calculation. Furthermore, based on this constitutive model, finite element models of masonry walls with six different masonry methods were built, and horizontal low-cycle reversed loading is applied to systematically study the variation patterns of wall ultimate strength, displacement, ductility, and stiffness. The results indicate that the staggered Flemish bond method exhibits peak loads 17.51% and 26.88% higher than those of the stretcher and header bond method and Sussex garden wall bond method, respectively, with its ductility performance being relatively limited. The findings of this study can provide foundational safety basis for advancing masonry construction from experience-based to performance-based design and comprehensively enhancing the seismic resilience of buildings in urban and rural localities in China.