Summary form only given. Plasma study at university level pulse power facilities as well as at the world's largest Z-pinch machines serves as one of the major drivers in the emerging topic of High Energy Density Physics. Plasmas created by 1 MA discharge at the university laboratories are very interesting and unique XUV and X-ray radiation sources that have extreme densities (nearing the solid state densities) and temperatures (in some cases exceeding 1 keV level). At such parameter range the dynamics and radiation performance features of these plasma objects are strongly dominated by the radiation effects such as the radiative cooling and radiation transport. Considering as an example wire array Z-pinch, one can estimate that near the current pulse maximum the radiation energy density becomes comparable with the specific internal energy of the precursor plasma column. At the same time the total radiation yield from z-pinch is several times higher than the plasma thermal energy. The main focus of this presentation is the study of radiation effects on the dynamics of high energy density plasma with the radiation MHD modeling. Dynamics of the precursor plasma column in imploding compact cylindrical wire arrays is discussed in greater details, while the simulation results are verified versus the experimental data. Particularly, the radiation MHD simulations demonstrate the transformation of precursor structure from uniform to heterogeneous as the precursor mass increases and radiation effects intensify. Novel wire ablation dynamics model has been used to account for wire material properties, such as the mass ablation rate. It is shown that by changing the wire materials one can control the parameters and radiation performance of the precursor column plasma. It is demonstrated that the flexibility of wire array load configuration provides the unique opportunities for a wide range of High Energy Density Physics experiments, particularly in the area of laboratory astrophysics.