The problem of nonstationary dynamic behavior of a disk weakened by a central cylinder-conic opening under the action of suddenly applied loading is considered. Determining relations are given in the form of a system of integral equations in an arbitrary oblique coordinate system. A numerical solution has been obtained by using a hybrid difference scheme constructed on the basis of the method of flow correction. Our generalized versions of the S.K. Godunov method for the case of a nonorthogonal system of coordinates were used as basic schemes. The locations of maximum stresses that precede the appearance of plasticity zones have been determined for a particular elastic body.