In offshore technology, especially in offshore wind energy converters, permanent deformations of the structures must be limited. For that purpose, the accumulation of permanent deformation due to cyclic loading must be predicted as accurately as possible. To account for this accumulation in non-cohesive soils, different approaches such as semi-empirical methods, p-y curve methods and numerical methods are available. Among the numerical approaches, the Stiffness Degradation Method (SDM) has the advantage of practical feasibility. However, it is only compatible with a relatively simple constitutive law and does not consider the influence of un- and reloading stress paths in the soil. With the basic concept of SDM, a new method termed Cyclic Strain Accumulation Method (CSAM) is proposed. In CSAM, the weaknesses of SDM, especially its incompatibility with advanced constitutive laws, are overcome, while retaining the practical feasibility as the main advantage of SDM. Through numerical calculations of a monopile, it is found that the CSAM is able to reproduce SDM results if the same material law is applied. The results of SDM and CSAM for the case of a vertical loaded strip footing have been presented. The comparison shows that the CSAM results are more realistic than the SDM results. Besides, CSAM is computationally more efficient and open for further optimisation. The effects of sophisticated material law and the consideration of un- and reloading are investigated. Results show that CSAM is a promising new approach to account for the deformation of foundations under cyclic loading in non-cohesive soils.