The Dense Z Pinch (DZP) configuration offers a potentially very compact form of fusion reactor. However it is unique among proposed reactors in its use of a high pressure (10 MPa) reaction region, requiring pressure vessel technology akin to that of the Pressurised Water Reactor (PWR). Neutron radiation damage to the vessel, and the large thickness of internal shielding which may consequently be required, are thus an obvious concern. In this paper we present calculations of vessel radiation damage and reactor power density for various sizes, reactor powers and internal shields. It is concluded that considerations of pressure vessel integrity will not prevent the operation of DZP reactors at power densities similar to those achieved in the PWR, and an order of magnitude greater than predicted for tokamak designs.