A two-dimensional elastic-plastic finite element analysis is performed for plane stress conditions with 4-node isoparametric elements to examine closure behaviour of fatigue cracks, giving special attention to the determination of the most appropriate mesh sizes. It is found that a smaller mesh size does not always give more accurate simulation results in the fatigue crack closure analysis, unlike a conventional structural analysis. A unique, most-appropriate mesh size exists for a given loading condition that will provide numerical results which agree well with experimental data. The most appropriate mesh size can be determined approximately in terms of the theoretical reversed plastic zone size. In particular, the ratio of the most appropriate mesh size to the theoretical reversed plastic zone size is nearly constant for a given stress ratio in the so-called crack-length-fixed method proposed in this study. By using the concept of the most appropriate mesh size, the finite element analysis can predict fatigue crack closure behaviour very well.