An infinitely long cylindrical cavity in an infinite elastic homogeneous and isotropic medium is enveloped by a plane shock wave whose front is parallel to the axis of the cavity. An integral transform technique is used to determine the stress field produced in the medium by the diffraction of the incoming shock wave by the cavity. Expressions for the radial stress σrr, the hoop stress σθθ, and the shear stress σrθ are derived as inversion integrals, and numerical results are presented for the time-history of the hoop stress σθθ at the boundary of the cavity. The amplifications of the hoop-stress concentration factors due to the dynamic loading are noted. The problem is considered for pressure waves with a step distribution in time. These results may be used as influence coefficients to determine, by means of Duhamel integrals, the stress field produced by waves with time-varying pressures.