Wave localization in a disordered periodic viaduct(DPV) undergoing out-of plane vibration is investigated.To this end, each span of the viaduct is simplified as a unit composed of a pier and two longitudinal beams.To investigate the wave localization in the disordered periodic viaduct, first the transfer matrix for the junction connecting two beams and one pier in one span of the viaduct is derived. Based on the transfer matrix for each span of the viaduct, the wave transfer matrix for each span is then constructed. By using the wave transfer matrices and Wolf's algorithm, the Lyapunov exponents for the wave localization in the viaduct can be determined. Using the proposed model, the influences of the pier-height and beam-length disorders on the wave localization are examined. In addition, the interactive effect of the damping in the pier and beam materials and the pier-height and beam-length disorders on the wave localization in a disordered viaduct are analyzed. Numeric results show that when pier-height and beam-length disorders occur, the Lyapunov exponents are almost unaffected by the lower frequency disorders. However, at increasing frequencies, the influences of the pier-height and beam-length disorders on the Lyapunov exponents becomes more significant. For the assumed parameters of the viaduct, in pass-bands, the damping of the piers and beams has a larger influence on the wave localization than the pier-height and beam-length disorders, while in the stop-bands, the disorders have a more pronounced influence on the wave localization than the damping.