This paper presents a very simple soil model of reduced dimensionality, that, using only two adjustable parameters, captures all the essential features of a set of six undrained cyclic torsional shear tests carried out on Toyoura sand by Oka and co-workers. The same values for all the model parameters (all but two of which are obtained from published data) are used for all six tests and very good agreement between the experimental test results and the simulations is achieved. Simulations of drained tests are also presented. The model uses a parameter that stores the recent strain history of the soil and that the authors show can be related to Houlsby's anisotropy parameter. The relationship between the volume and shear strain increments contains two terms. The first term simulates continual compaction while the second can predict additional compaction or dilatancy, depending on the direction of the shear strain increment. These two terms cancel each other out during continuous deformation at the critical state, but reinforce each other on reversal to predict the rapid densification observed experimentally.