The present paper points out that Kromm’s [1] plane-stress solution, for compressional waves in an infinite elastic plate subjected to radial pressure in a circular hole at its center, has application to still another problem of interest. This is the problem of a stretched elastic plate in which a circular hole is suddenly punched. The plane-stress solution for the tensile circumferential stresses, generated by the unloading mechanism in punching, is given here. This solution is derived independently of Kromm’s work in which a rather special Laplace-transform technique was used. The derivation given here also makes use of the Laplace transform but in a more direct manner, employing the inversion integral and a contour integration. It is also shown that the present inversion technique offers important simplifying features over that used by Selberg [3] in the closely related plane-strain problem. The numerical results presented are of interest in fragmentation studies. It is shown that the dynamic circumferential stress field in the vicinity of the punched hole is quite severe; which would be important to the creation and propagation of radial cracks.