Dynamic steady-state spherical cavitation fields are examined with emphasis on material porosity at large strain. Cavity expansion is driven by constant internal pressure in presence of remote tension or compression. The plastic branch of constitutive relations is described by the Gurson model, with arbitrary strain hardening. The mathematical model is reduced to a system of four ordinary nonlinear coupled differential equations. Numerical examples show that a plastic shock wave builds up as expansion velocity approaches a critical value and jump conditions across the shock are accounted for. At critical levels of remote tension, quasi-static cavitation of all internal voids is induced before dynamic cavity expansion occurs.