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Interstellar dust penetrates into the heliosphere/astrosphere due to relative motion of the Sun and the local interstellar medium (LISM). Inside the heliosphere/astrosphere and at the heliospheric boundaries, where the solar/stellar wind interacts with LISM, distribution of the interstellar dust is modified due to an action of electromagnetic forces, the solar gravitation and radiation pressure. In this paper we show that the distribution of the interstellar dust particles in the heliosphere has peculiarities of high density layers. In order to understand the nature of the peculiarities Osiptsov's Lagrangian method has been employed and developed for the case when the force acting on the particles has discontinuity as it is for the electromagnetic force at the helioshperic current sheet. In the result of the modeling we demonstrate existence of multiple layers of high density of the interstellar dust located at 0.03 - 10 AU north and south with respect to the heliospheric current sheet. This work has been supported by the Ministry of Education and Science of Russian Federation grant 14.W03.31.001