According to the situation that both the polluted layer and the unpolluted layer in the Yangtze River pollution are in confined aquifer, by using Darcy theorem and quality conservation law, the mathematical model of three-dimensional coupled parabolic equation system is set up, based on the basic theory of partial differential equation, by using integral mode, the three dimensional mathematical model is reduced into a two-dimensional model, by constructing truncation function and the operator satisfying consistency conjecture, via using Schauder theorem, the existence of the two-dimensional mathematical model solution is proved, so that the feasibility of critical interface between the polluted water layer and the unpolluted water layer of the Yangtze River pollution problem in the confined aquifer is proved, which provide theoretical basis for studying water pollution problem of the Yangtze River.