We present a statement of an automodel problem about motion of an elastic body in an elastic cavity. The body is of wedge shape with an arbitrary value of the angle of the wedge. We reduce the process of solution of the problem to summation of infinite trigonometric series. We obtain different solutions for the following regions: (1) a circle with the center at a tip of the wedge; (2) a ring contacting the circle mentioned; (3) a domain that is outer with respect to the ring mentioned.