A computational method is presented for the assessment of rupture probabilities in soft collagenous tissues. This may in particular be important for the quantitative analysis of medical diseases such as atherosclerotic arteries or abdominal aortic aneurysms, where an unidentified rupture has in most cases fatal consequences. The method is based on the numerical minimization and maximization of probabilities of failure, which arise from random input quantities, for example, tissue properties. Instead of assuming probability distributions for these quantities, which are typically unknown especially for soft collagenous tissues, only restricted knowledge of these distributions is taken into account. Given this limited statistical input data, the minimized/maximized probabilities represent optimal bounds on the rupture probability, which enable a quantitative estimation of potential risks of performing or not performing medical treatment. Although easily extendable to all kinds of mechanical rupture criteria, the approach presented here incorporates stretch-based and damage-based criteria. These are evaluated based on numerical simulations of loaded tissues, where continuum mechanical material formulations are considered, which capture the supra-physiological behavior of soft collagenous tissues. Numerical examples are provided demonstrating the applicability of the method in an overstretched atherosclerotic artery.