Strong S waves produce dynamic stresses, which bring the shallow subsurface into nonlinear anelastic failure. The construct of coulomb friction yields testable predictions about this process for strong‐motion records. Physically, the anelastic strain rate increases rapidly with increasing dynamic stress, and dynamic stress is proportional to the difference between total strain and anelastic strain. Nonlinear models of vertically propagating S waves in layered media confirmed and illustrated analytical inferences. The effective coefficient of friction bounds (clips amplitude) the resolved horizontal acceleration normalized to the acceleration of gravity. There is a tendency for the random signal from vertically propagating S waves to become transiently circularly polarized at the maximum (clipped) resolved acceleration, as the acceleration component perpendicular to the current acceleration adds weakly the resolved acceleration. Frictional attenuation does not preferentially suppress high‐frequency signal; it cannot be modeled by increasing ordinary linear attenuation. In addition, an effect of shallow cohesion is to allow brief pulses of strong high‐frequency acceleration to reach the surface. Frictional attenuation within deep overpressured aquifers suppresses shaking recorded at the surface, but does not simply clip amplitude at a given resolved acceleration. The anelastic strain rate increases slowly with stress within shallow muddy sediments. The accelerations from reverberations within such layers can exceed .