Abstract: Uncertainty and sensitivity analysis of the nuclear system is of great significance for reducing the design margin of nuclear design and improving the economics of the nuclear system. The sampling method for the uncertainty and sensitivity analysis is becoming more and more important because of its simple algorithm, taking into account high-order effects, and no special requirement for response parameters. However, it was previously considered that it was difficult to analyze the sensitivity coefficient based on the statistical sampling method. The main reason was that the change of the response was caused by the simultaneous change of the multivariate, and it was difficult to determine the change of the response caused by the change of a single variable. In this paper, the theoretical formula of sensitivity coefficient analysis using statistical sampling method was deduced firstly. Then the critical formula of bare reactor with two groups approximation and the PWR cell TMI benchmark were verified, and the feasibility of the method was verified. In order to deal with the difficulty of inversion of the covariance matrix of the actual problem, the simplified covariance matrix and the unified perturbation method were proposed in this study, and the two alternative solutions were verified by using the ²³⁵U fission cross section. The analysis proves the feasibility of the method. At the same time, the influence of different sensitivity coefficients on the TMI infinite multiplication factor uncertainty was also analyzed.