ObjectiveThe aim of this study was to assess whether aortic peak wall stress (PWS) and peak wall rupture index (PWRI) were associated with the risk of abdominal aortic aneurysm (AAA) rupture or repair (defined as AAA events) among participants with small AAAs.MethodsPWS and PWRI were estimated from computed tomography angiography (CTA) scans of 210 participants with small AAAs (≥ 30 and  ≤ 50 mm) prospectively recruited between 2002 and 2016 from two existing databases. Participants were followed for a median of 2.0 (inter-quartile range 1.9, 2.8) years to record the incidence of AAA events. The associations between PWS and PWRI with AAA events were assessed using Cox proportional hazard analyses. The ability of PWS and PWRI to reclassify the risk of AAA events compared to the initial AAA diameter was examined using net reclassification index (NRI) and classification and regression tree (CART) analysis.ResultsAfter adjusting for other risk factors, one standard deviation increase in PWS (hazard ratio, HR, 1.56, 95% confidence intervals, CI 1.19, 2.06;p= 0.001) and PWRI (HR 1.74, 95% CI 1.29, 2.34;p< 0.001) were associated with significantly higher risks of AAA events. In the CART analysis, PWRI was identified as the best single predictor of AAA events at a cut-off value of  > 0.562. PWRI, but not PWS, significantly improved the classification of risk of AAA events compared to the initial AAA diameter alone.ConclusionPWS and PWRI predicted the risk of AAA events but only PWRI significantly improved the risk stratification compared to aortic diameter alone.Key Points• Aortic diameter is an imperfect measure of abdominal aortic aneurysm (AAA) rupture risk.• This observational study of 210 participants found that peak wall stress (PWS) and peak wall rupture index (PWRI) predicted the risk of aortic rupture or AAA repair.• PWRI, but not PWS, significantly improved the risk stratification for AAA events compared to aortic diameter alone.Supplementary InformationThe online version contains supplementary material available at 10.1007/s00330-023-09488-1.