The mechanical behavior at soil–structure interface (SSI) has a crucial influence on the safety and stability of geotechnical structures. However, the behavior of SSI under constant normal stiffness condition from micro- to macro-scale receives little attention. In this study, the frictional characteristics of SSI and the associated displacement localization under constant normal stiffness condition are investigated at both macro- and microscales by simulating a series of interface shear tests with discrete element method. The algorithm to achieve a constant normal stiffness is first developed. The macroscopic mechanical response of the interface shear tests with both loose and dense specimens at various normal stiffness is discussed in terms of shear stress, normal stress, vertical displacement, horizontal displacement and stress ratio. Then, the microscopic behaviors and properties, including shear zone formation, localized void ratio, coordination number, force chains and soil fabric, are investigated. The effect of normal stiffness is thus clarified at both macro- and microscales.