The article presents an algorithm for modeling diffraction on slits made on a flat screen made of actual materials. As a result, the boundary conditions of Schukin-Leontovich lead to the mixed boundary value problem. According to the method of Y.V. Gandel and V.D. Dushkin the solution of the problem can be reduced to a system of paired integral equations with singular and logarithmic singularities. The author has created and debugged a PC program that performs the numerical solution of the arising problems, and a series of computational experiments has been performed. This work has been carried at School of Mathematics and Computer Sciences of V. N. Karazin Kharkiv National University within the state budget themes: "Modeling of the dynamics of folding systems with the method of identifying problem situations".