We explore the possible stress triggering relationship of the M >= 6.4 earthquakes that occurred in Kerman Province, southern Iran since 1981. We calculated stress changes due to both co-seismic sudden movement in the upper crust and the time-dependent viscous relaxation of the lower crust and/or upper mantle following the event. Four events of M >= 6.4 occurred between 1981 and 2005, on and close to the Gowk fault, show a clear Coulomb stress load to failure relationship. The 2003 M = 6.5 Bam earthquake, however, which occurred approximately 95 km SW of the closest Gowk event, shows a very weak stress relation to preceding earthquakes. The coseismic static stress change at the hypocentre of the Bam earthquake is quite small (similar to 0.006 bars). The time-dependent post-seismic stress change could be 26 times larger or 7 times lower than that of coseismic static stress alone depending on the choice of viscoelastic crustal model and the effective coefficient of friction. Given the uncertainties in the viscoelastic earth models and the effective coefficient of friction, we cannot confidently conclude that the 2003 Bam event was brought closer to failure through coseismic or post-seismic stress loading. Interestingly, the southern Gowk segment with a similar strike to that of the Bam fault, experienced a stress load of up to 8.3 bars between 1981 and 2003, and is yet to have a damaging earthquake.