To investigate the feasibility of installing embedded rail tracks for trams on continuous beam bridges, an embedded rail track-bridge element model is proposed, and a static model of continuous welded rail (CWR) system is established for the bridge structure. The longitudinal forces and deformations of the CWR system under bridge temperature loads are analyzed. Using beam-rail relative displacement as the evaluation criterion, this study assesses the feasibility of CWR installation schemes and examines the effects of annual bridge temperature variation, longitudinal resistance of polymer materials, and rail expansion joint configurations on the mechanical behavior of the CWR system. Results indicate that the annual bridge temperature difference significantly affects both the beam-rail relative displacement and rail additional expansion force, exhibiting an approximately linear increase with temperature variation. Maximum values of both parameters occur at the right beam joint of the second continuous beam bridge. With an annual temperature difference of 30℃, the beam-rail relative displacement reaches 12.79 mm, exceeding the allowable limit of 6.20 mm. Since adjusting the longitudinal resistance of polymer materials proves insufficient to maintain displacement within limits, rail expansion joints are required. The installation of grooved rail expansion joints at the right beam ends of both the 11th and 19th spans is recommended to ensure acceptable beam-rail relative displacement.