We consider a layer of finite thickness loaded in plane strain by a stamp with a straight horizontal base, which is smooth and rigid. The stamp is pressed vertically into the layer and is slightly rotated by an external moment load subsequently. Two cases are considered successively: the lower side of the layer is attached to a rigid base and, secondly, the lower side is allowed to slide without friction along the base. The paper is divided into two parts. The first part deals with an asymptotic investigation of a thin layer and the second one refers to a thick one.