A rate dependent (viscoplastic) soil model [1] based on the subloading surface overstress concept proposed by Hashiguchi [2], revised and generalised to cyclic loading conditions (abrupt changes in loading direction) was formulated to reproduce complex experimentally revealed features of real soil behaviour so that they can be used to predict the response of geotechnical structures. In the limit, when the viscosity tends to zero, an elastoplastic subloading surface model with some distinct features is recovered. This form of elastoplasticity does not have a large elastic domain and produces a smooth transition from elastic to plastic response, unlike traditional hardening elastoplastic models. Some significant flaws of other improved model formulations, such as the bounding surface, the two surface (bubble) or the hypoplastic ones, are also avoided. Both the time rate dependent and plastic versions of the model include initial and induced inelastic anisotropy, and cementation (bonded particles). It was also extended to soil-rockfill mixtures, temperature dependency and unsaturated behaviour. Model simulations of the subloading models described are presented that show their ability to reproduce experimental soil response with significant accuracy under such distinct conditions such as: time rate changes, cementation, soil-rockfill mixtures, non isothermal and unsaturated.