A highway bridge located in Tampico, on the east coast of Mexico, is analyzed to determine its structural reliability against wind loading. The inherent variabilities of the random wind force and of the mechanical properties of steel constitute the aleatory uncertainty; this contributes to the probability of failure of the steel girder. The idealization of the loading and of the bridge structure, and the analysis of the structural response to wind loading, contribute to additional uncertainty of the epistemic type, which leads to a range of possible (or distribution of) failure probabilities. The design with the minimum expected life-cycle cost is the optimal design. However, for this optimal design, the 90% value (or the mean plus one standard deviation value) of the corresponding failure probability or safety index may be selected for a risk-aversive design. The proposed criteria constitute a new approach to make conservative decisions and involve the epistemic uncertainty on the bridge design and assessment process