Expected utility theory can be relevant for decision-making under risk, when different preferences should be taken into account. The goal of this paper is to present a quantitative risk analysis methodology, depending on expected utility, where the risk consequences are determined quantitatively, the risk is modelled using a loss random variable and the expected utility loss is used to classify and rank the risks. Considering the relevance of risk management to reduce workers' exposure to occupational risks, the methodology is applied to the analysis of accidents in industry, where six different injury categories are distinguished. The ranking of the injury categories is determined for three different utility functions. The results indicate that the slope of the utility function influences the ranking of the injury categories. The choice of the utility function may thus be relevant for the risk classification in order to prioritize different aspects of risk consequences.