Argon based capillary discharge lasers operating in the extreme ultra violet (EUV) at 46.9 nm output up to 0.5 mJ energy per pulse at up to 10 Hz repetition rates are capable of focussed irradiances of 10 9 -10 12 W cm −2 and can be used to generate plasma in the warm dense matter regime by irradiating solid material. To model the interaction between such an EUV laser and solid material, the 2D radiative-hydrodynamic code POLLUX has been modified to include absorption via direct photo-ionisation, a super-configuration model to describe the ionisation dependant electronic configurations and a calculation of plasma refractive indices for ray tracing of the incident EUV laser radiation. A simulation study is presented, demonstrating how capillary discharge lasers of 1200 ps pulse duration can be used to generate warm dense matter at close to solid densities with temperatures of a few eV and energy densities up to 1 × 10 5 J cm −3 . Plasmas produced by EUV laser irradiation are shown to be useful for examining the properties of warm dense matter as, for example, plasma emission is not masked by hotter, less dense plasma emission as occurs with visible/infra-red laser target irradiation.