The calculation of water permeability through a system of defects (long narrow slits in the junctions) in the screen is considered based on the filtration model. Its structural layout and description of the model main elements are given. The solution is carried out for the plane formulation of the problem by the methods of the filtration theory using the method of conformal mappings and the velocity hodograph method. A distinctive feature is the study of free filtration through a system of screen slits (the isolated standard fragment with a single defect), characterized by a pressure movement of the filtration flow in the protective layer and pressure/pressure-free movement at the bottom of the screen, taking into account the mutual influence of the slits on each other. We obtained the calculated dependences for the determination of the specific filtration flow through the screen slit, as well as the total flow through the system of slits and the averaged screen filtration factor, the results of the calculations are compared to the known formulas for the defect system. For practical use, a table of averaged screen filtration factors and a graph of the change in the reduced flow rate through the screen, considering and not considering the influence of the underlying base are made.