Static stress transfer is one physical mechanism to explain triggered seismicity. Coseismic stress‐change calculations strongly depend on the parameterization of the causative finite‐fault source model. These models are uncertain due to uncertainties in input data, model assumptions, and modeling procedures. However, fault model uncertainties have usually been ignored in stress‐triggering studies and have not been propagated to assess the reliability of Coulomb failure stress change (ΔCFS) calculations. We show how these uncertainties can be used to provide confidence intervals for co‐seismic ΔCFS‐values. We demonstrate this for the MW = 5.9 June 2000 Kleifarvatn earthquake in southwest Iceland and systematically map these uncertainties. A set of 2500 candidate source models from the full posterior fault‐parameter distribution was used to compute 2500 ΔCFS maps. We assess the reliability of the ΔCFS‐values from the coefficient of variation (CV) and deem ΔCFS‐values to be reliable where they are at least twice as large as the standard deviation (CV ≤ 0.5). Unreliable ΔCFS‐values are found near the causative fault and between lobes of positive and negative stress change, where a small change in fault strike causes ΔCFS‐values to change sign. The most reliable ΔCFS‐values are found away from the source fault in the middle of positive and negative ΔCFS‐lobes, a likely general pattern. Using the reliability criterion, our results support the static stress‐triggering hypothesis. Nevertheless, our analysis also suggests that results from previous stress‐triggering studies not considering source model uncertainties may have lead to a biased interpretation of the importance of static stress‐triggering.