Cyclic axial loads effects have long been recognized as one of the most significant actions that pile foundations of offshore structures have to withstand during its useful life. In spite of that there is no consensus in the best approach to assess its effects. In this work the CPT-based effective stress ICP (Imperial College Pile) method was used to evaluate the cyclic axial resistance by suitably combining it with an accumulation procedure that progressively accounts for the local reduction in radial effective stress acting on the shaft. In the first stage the soils involved were characterized in terms of the reduction of effective stress observed in Cyclic Direct Simple Shear tests (DSS, ASTM D6528). Secondly, following the ICP method, the reduction in axial load is computed from the local reduction of the effective radial stress along the pile shaft. This involves the discretization of piles with elastoplastic degrading t-z curves. The global effect along the pile is computed and the results are summarized in terms of cyclic interaction diagrams. The procedure provides a robust approach that considers the main aspects of cyclic response, including the progressive degradation of resistance along the shaft during the load history. This procedure was applied to a real case of piles driven in a variable soil profile in the Mexican Gulf of Mexico area.