Nonlinear site‐response analyses are becoming an increasingly important component of simulated ground motions for engineering applications. For regional‐scale problems for which geotechnical data are sparse, the challenge lies in computing site response using a very small number of input parameters. We developed a nonlinear soil model that, using only the shear‐wave velocity profile, captures both the low‐strain stiffness and large‐strain strength of soils and yields reliable predictions of soil response to weak and strong shaking. We here present the formulation of the model and an extensive validation study based on downhole array recordings, with peak ground acceleration (PGA) ranging from to . We also show that our model, referred to as hybrid hyperbolic (HH), outperforms existing nonlinear formulations and simplified site‐response analyses widely used in practice for ground motions that induce more than 0.04% of soil strain (roughly equivalent to PGA higher than ). In addition to site‐specific response predictions at sites with limited site characterization, the HH model can help improve site amplification factors of ground‐motion prediction equations (GMPEs) by complementing the empirical data with simulated site‐response analyses for very strong ground shaking, as well as physics‐based ground‐motion simulations, particularly for deeper sedimentary sites with low resonant frequencies.