Stress history and loading path can significantly influence the cyclic response of sands. It is well known that cyclic behaviour under non-symmetrical cycling is generally different from that under symmetrical loading around zero deviator stress. Anisotropic consolidation prior to cycling in triaxial apparatus changes the behaviour by exerting an initial static shear stress on critical planes. The present paper reports the results from a number of cyclic triaxial tests on anisotropically consolidated samples of Sydney beach sand. The samples are reconstituted in the laboratory and subjected to non-reversal cycling in compression only loading under undrained conditions. Typical test behaviours are described and the effects of cyclic stress ratio and initial state on the response are discussed. It is shown that the state parameter is capable of predicting the cyclic resistance and the trend of excess pore water pressure generation during one-way compressional cycling and, as has been well established for simple loading paths, critical state soil mechanics is able to provide a reliable framework to characterize the behaviour under different cyclic loading conditions.