Nonlinear waves in a bilinear soil layer are described for excitation by vertically arriving S-wave pulses of strong ground motion. Conditions that lead to the nonlinear deformation are described in terms of amplitudes and wavelengths of incident pulses. It is shown that the layer can fail during the first passage of the incident wave (during a time shorter than the travel time through the layer). Peak amplitudes of (1) transient rotations, of (2) permanent rotations (strains), and of (3) the peak ductility in the layer are described in terms of the dimensionless amplitudes of incident pulses and the places of their occurrence in the layer. Even a simple model like this (one-dimensional propagation, simple shape of incident pulse, bilinear stress-strain soil model) leads to very complicated response. The results presented offer only a glimpse at the complexity in a realistic setting.