In the proposed study, the fatigue analysis of an axisymmetric chiral cellular structure and its modified form, made of stainless steel 316L, is carried out. The main goal of the original structure geometry was to absorb as much mechanical energy as possible with its auxetic behaviour. However, it was found through testing that its response could be improved by modifying the thickness of the struts through the structure. Representative models for the original and modified geometries were generated using a script adapted for this numerical simulation. Three different types of displacement in the shape of sine waves were used to load the structures. A hexagonal mesh was assigned and determined by convergence analysis. An existing material model with the necessary LCF parameters was assigned in the computational analyses. The data from multiple simulations were recorded and presented in graphs that showed how the fatigue life of the structures changed depending on the level of strain. We also analysed stresses and plastic deformations that occur in the structures. The results showed that, despite a better stress distribution, the fatigue life of the optimised structure was shorter in all cases.