In the paper, stress state of an elastic, isotropic and homogeneous weighty half-plane weakened by an elliptic hole with two rectilinear cracks is considered. The domain S occupied by a body consists of a "lower" half-plane bounded by the straightline L 2 and a contour of the hole L 1 . The elastic medium, in addition to its specific weight at the infinity is subjected to the action of uniformly-distributed pressure of intensity q on the segment -a< t < a of a rectilinear boundary L 1 of the

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... f-plane. The hole's contour is free from external forces. Many aspects of such problems have been considered in the papers[1; 3; 6; 7; 8; 10]. But the case that we investigate is considered for the first time (this is connected with definition of the mapping function and also complexity of acting force factors).