Hydraulic structures are designed with reference to some natural events which could be imposed on the structure during its expected service life. Conventionally return period design methods fail to systematically account for the many uncertainties in design. By systematically analyzing the component uncertainties and their interactions using the concepts of reliability theory and first-order analysis of uncertainties, a composite risk and reliability can be defined. This paper presents static and dynamic risk and reliability models that can be used to develop risk-safety relationships for various return periods and expected service lifes that can be used in design. The static models consider single loading application and the dynamic models consider repeated application of random loadings to define a composite risk. The models are applied as examples of the methodology to develop risk-safety curves for culvert design. This work presents a scientific approach to systematically account for the uncertainties and their interactions in the selection of safety factors and return periods for various risk levels in hydraulic design.