The following filtration currents with unknown free boundaries are investigated: under a hydro- engineering structure with the regions of constant velocity of the flow in the presence of a water thrust of a complicated configuration; under a rabbet of Zhukovsky through an irrigated ground area with a substratum of a strongly permeable pressure head horizon, the left semi-infinite part of the roof of which is modeled by an impenetrable inclusion; and from channels through a soil stratum with an underlying well permeable water-bearing horizon, taking into account the capillarity of the ground and evaporation from the free surface. To study them, mixed multi-parameter boundary value problems of the theory of analytical functions are formulated and solved.
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