New railway bridges for high-speed trains are being built in a many countries around the world. In addition to the construction of new bridges, existing bridges are ageing. These two factors make the assessment of railway bridges essential. The bridges are designed considering certain predefined reliability criteria to account for the variability in load and resistance. However, for the assessment of these bridges, a probabilistic analysis of the structure in the presence of uncertainties is recommended. This thesis presents a probabilistic analysis of a railway bridge based on a case study of a newly constructed bridge. In the analysis performed, uncertainties in concrete material properties are incorporated. Given the unavailability of measured data in the location of bridge construction, expert judgment elicitation is carried out to estimate for the uncertainties in loading conditions of a train. Further, these uncertainties are incorporated in a finite element analysis to estimate the bridge response in the form of shear force and bending moment. The variables corresponding to the maximum shear force and the maximum bending moment, as well as the loading conditions and the material properties, are then merged into a Non-Parametric Bayesian Network. Conditionalization of the developed Bayesian networks is carried out to draw inferences on the bridge response when evidence on load or material properties is known. It is shown that expert judgment elicitation can be applied for risk assessment of railway bridges. Further, the developed Non-Parametric Bayesian network can be used to estimate and update the probability of failure. Improvements to this study can be made by updating the probability of failure in the event of an earthquake.