Abstract: Experimental evidence has shown that the mechanical behavior of normally consolidated clay-structure interfaces differs significantly from that of a homogeneous soil medium. Specifically, the interface shear strength decreases as the shear rate increases, and the shear strength exhibits pronounced softening under slow shear conditions. These unique mechanical characteristics cannot be adequately captured by traditional elastoplastic interface models. This paper develops an elastic viscoplastic model designed to describe the influence of shear rate and normal stress on the shear behavior of interfaces between normally consolidated clay and structure plate. The model includes three key features: the application of overstress theory to account for the viscous behavior of clay-structure interfaces, the transfer of the failure plane from the clay inside to the interface to capture the softening phenomena in interface shear testing, and the integration of the critical state framework for clay-structure interfaces with an analytical solution of pore pressure dissipation to illustrate the effects of shear rate under drained and partially drained conditions. Moreover, an explicit numerical scheme is proposed to simulate the coupled mechanical and hydraulic behaviors with the pore pressure generation and dissipation processes. To validate the model, various interface tests with different shear rates and under creep condition are simulated. Comparisons between experimental data and simulation results demonstrate a good predictive ability of the proposed elastic viscoplastic model for clay-structure interfaces.