The problem of embedding of two rigid symmetric elliptic stamps into a thick elastic layer to a given depth is considered. The asymptotics of the stress concentration function is constructed under the base of the stamp. It depends on two parameters: the relative distance between the centers of the stamps and the relative thickness of the layer. Two types of boundary conditions are considered: a layer on a rigid base without friction, and the lower plane of the layer is rigidly connected to the base. The analysis of the solutions obtained is carried out for the different values of the parameters mentioned.
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