A cyclic loading with multidimensional strain loops in the soil may be caused by traffic loading, by wind and wave loading (e.g. offshore wind turbines) or by earthquake shaking. The present paper focuses on the accumulation of permanent deformations due to a high-cyclic loading, that means a loading with many cycles of small to intermediate strain amplitudes. Two different strategies for the consideration of multidimensional strain loops in a high-cycle accumulation model are presented. Experimental evidence for the first strategy is provided. However, it is suitable for convex strain loops only. The second strategy can handle also non-convex strain loops, but has not been confirmed experimentally yet. The paper discusses suitable experiments for such prove and documents some preliminary test series.