In the face of the pressing environmental issues, the past decade witnessed the booming development of the distributed energy systems (DESs). A notable problem of DESs is the inevitable uncertainty that may make DESs deviate significantly from the deterministically obtained expectations, in both aspects of optimal design and economic operation. It thus necessitates the sensitivity analysis to quantify the impacts of the massive parametric uncertainties. This paper aims to give a comprehensive quantification, and carries out a multi-stage sensitivity analysis on DESs from the perspectives of evaluation criteria, optimal design and economic operation. First, a mathematical model of a DES is developed to present the solutions to the three stages of the DES. Second, the Monte-Carlo simulation is carried out subject to the probabilistic distributions of the energy, technical and economic parameters. Based on the simulation results, the variance-based Sobol method is applied to calculate the individual importance, interactional importance and total importance of various parameters. The comparison of the multi-stage results shows that only a few parameters play critical roles while the uncertainty of most of the massive parameters has little impact on the system performance. In addition, the influence of parameter interactions in the optimal design stage are much stronger than that in the evaluation criteria and operation strategy stages.