The equation of motion governing the response of long (infinite) cylinders to dynamic internal pressures is derived. Since large displacements and wall-thinning effects are taken into account, elastic behavior of the material is neglected. The material is assumed to be rigid-plastic, with strain-hardening being taken into account through the Ludwik power strain-hardening law. Numerical results are presented for a range of hardening constants from 0.01 to 1.0, covering the range applicable to most materials of interest. The form of the dynamic pressure considered is an initially peaked, linearly decaying pressure pulse. Charts are presented giving the pressure and duration required to produce a given final radius of the cylinder.