This chapter discusses the modelling of stress-strain relationships of soils; hysteretic stress-strain curves and their equivalent linearization, the modeling of dilatancy, and the definition of cyclic strength in seismic loading. It outlines numerical methods using these models in terms of their aims, distinctions and numerical schemes. The chapter aims to compare the equivalent linear analyses and stepwise nonlinear analyses with the dynamic response of sand layers in shaking table tests to characterize the analytical results. It then addresses shaking table model tests and associated similitudes together with soil properties in scaled models under very low confining pressures. Nonlinear stress-strain curves of soils under cyclic loading are idealized by simple functions. Among them, bilinear, hyperbolic and Ramberg-Osgood models are representative in many engineering problems. In order to construct the stress–strain relationship under cyclic loading, the Masing rule is incorporated to extend the skeleton curve to the hysteretic curve corresponding to cyclic stress changes.