Seismic fault failure can generate additional static stress in surrounding solid medium. The stress change, calculated by using certain fault model and following Coulomb fracture criteria, with the aim at testing if it can trigger other fault failures, is called Coulomb failure stress (CFS) change. It is commonly believed that the CFS change generated by an earthquake can affect the occurrence of other remote earthquakes. This paper examines and compares the calculations of CFS change in using three different models. Since the Volterra dislocation model can not accurately represent the source parameters, the additional static stress field given by this model has major flaws. The linear elastic fracture mechanics model can be related to the real stress drop, but can not give the limit range of the source parameters. In addition, it also has the problem of stress singularity at crack ends. The slip-weakening model not only eliminates the stress singularity, but also gives more reasonable constraints on source parameters. However, quantitative analysis shows that in calculating CFS changes the rationality of the fault model must be taken into account, and that for any above model the calculated CFS change induced by a major earthquake in far field is very low, being not enough to influence the occurrence of another remote earthquake. Up to now rock experiments and actual observations do not support the hypothesis that the Coulomb stress generated by an earthquake can affect the occurrence of a next remote earthquake. Therefore, we need to find new ways to interpret the remote correlation of seismic activities around the world and the cause of static remote triggering of major earthquakes.