This paper presents one-dimensional ground response simulations of centrifuge models involving soft clay deposits subjected to ground motions of varying intensity. Total stress ground response simulations were performed using equivalent-linear (EL) and nonlinear (NL) methods. Shear strains higher than 10% were mobilized during large ground motions; therefore, undrained shear strength of the clay is an important parameter for the simulations. Testing shows that the San Francisco Bay Mud materials used in centrifuge modeling have monotonic shear strengths that increase by 13% per log cycle of shear strain rate. A comparison of simulation results to observations reveals the importance of incorporating shear strength into the development of stress-strain backbone curves, with appropriate consideration of rate adjustments to shear strength and stiffness. NL ground response simulations provide a good match to observed pseudospectral accelerations only when rate-adjusted shear strengths are properly accounted for; otherwise, the NL simulations have significant underprediction bias at oscillator periods less than the soil column period. EL modeling, even with the incorporation of shear strength, leads to unrealistic spectral shapes and overprediction at short spectral periods for tests involving large-strain site response.