The interaction between the surface and underground waters is often a point of interest in land reclamation, engineering hydrology, and hydrogeology. Thus, the paper deals with modeling the process of unsteady fluid filtration in a sandwich-type reservoir system. Such a study is very relevant for Uzbekistan, where these kinds of soil structures are quite common. The mathematical model of fluid filtration was developed based on partial differential equations of parabolic type with boundary conditions. An analytical solution to the problem was found using the Laplace transform. The computational experiments were carried out to determine the changes in pressure along the filtration layers' length without taking into account the elastic regime. It was found that the pressure in both layers increases exponentially. The flow of water through the interface of the filtration layers significantly depends on the piezo conductivity coefficient of a well-permeable layer, as well as on the filtration coefficient of a slightly permeable layer. There was obtained the analytical solution of the problem of fluid filtration in a sandwich-type reservoir system. The solution of the problem of determining the pressure in a weakly permeable filtration layer was found. And a new generalized formula for well gallery control was derived. The developed mathematical tool allows users to draw up the schemes of location and capacity of vertical drainage wells to protect irrigated and non-irrigated areas from flooding and protect groundwater from pollution sources, as well as isolate already contaminated areas.