The Coulomb failure function (CFF) quantitatively describes static stress changes in secondary faults near the source fault of an earthquake. CFF can be employed to monitor how static stress transfers and then shed some light on the probability of successive events occurring around a source fault. In this paper we focus on the CFF and particularly on optimally oriented planes. We present a unified model to determine an optimally oriented plane and its corresponding Coulomb stress, then apply the model to the 2003 Mw 6.6 Bam (Iran) earthquake and the 2008 Mw 7.9 Wenchuan (China) earthquake, thereby checking its effectiveness. Our results show that spatial correlation between positive Coulomb stress changes and aftershocks are, for the 2003 Bam earthquake, 47.06% when elastic Coulomb stress changes are resolved on uniform planes and 87.53% when these are resolved on optimally oriented planes at depth; for the 2008 Wenchuan earthquake the correlations are 45.68% and 58.20%, respectively. It is recommended that account be taken of optimally oriented planes when drawing a Coulomb stress map for analyzing earthquake triggering effects.