A description has been given of the general features of the cap model as used to represent geological materials. In addition, the theoretical basis for the model has been indicated and a particular example of the model has been presented. The model is intended to represent the behavior of a wide range of geological materials in problems for which the nonlinear hysteretic nature of such materials is significant. Although the primary area of application of the model in the past has been in the numerical computation of ground shock effects in layered sites due to explosive sources, the model should be applicable to other fields of interest such as earthquakes and various types of penetration into soils and rocks.