Abstract: Structural influence line identification is the theoretical basis of evaluation for an existing structure under moving loads, which is essentially to identify the response function of a specified section of a static system based on finite dimensional input-output noisy data. Despite progress in previous researches, there are limitations in two aspects, i.e., lack of identifiability analysis of inverse problem and lack of Uncertainty Quantification (UQ). The identifiability analysis of the inverse problem is to clarify the solution situation of the parameters. UQ is to estimate the posterior probability density function (PDF) of the influence line based on the measured input-output noisy data. For these two limitations, this paper conducts the inverse problem identifiability analysis and Bayesian UQ of influence line identification based on Bayesian probability framework. This paper identifies influence lines based on direct parameterization, including system input and output, inverse problem identifiability analysis and optimal values of parameters. The results show that: direct parameterization cannot guarantee that the model is globally model-identifiable; even if the model is globally model-identifiable, the existing methods can only obtain the optimal values of the parameters. In order to ensure the globally model-identifiable case and to obtain the posterior PDF of the parameters simultaneously, the posterior identification of influence lines based on reduced-dimension Bayesian UQ is proposed, including system input and output reconstruction, inverse problem identifiability analysis and posterior PDF. The effectiveness of the proposed method is verified by identifying the influence lines of the suspender force of the Xinguang Bridge using simulated data, and the influence lines of the strain of a simply supported beam bridge using measured and simulated data.