Knowledge of thermodynamic properties of materials in a warm dense region is especially important for us to understand many high-energy density physics processes and phenomena, such as the interior structure of the earth, inertial confinement fusion, and the formation and evolution of supernovas and gaseous giants. Because of the simple filled-shell electronic configuration, neon (Ne) and krypton (Kr) can be well used as standard test cases for the thermodynamic properties studies, including the equation of state (EOS), metallic transition, and so on, in a warm dense region. Moreover, Ne is the primary constituent of planetary and stellar atmospheres. Its thermodynamic properties in the WDM region are also vital to construct the inner structure of these astrophysics objects and understand their formation and evolution, which have attracted increasing interest in astrophysics studies. And Kr is one of the products of nuclear fission. Its dynamic structure and electronic behavior will directly affect the progress of nuclear reactors. In this work, multiple shock reverberation compression experiments are designed and performed to determine the equation of state of neon and krypton ranging from the initial dense gas up to the warm dense regime where the pressure is from about 10 MPa to 160 GPa and the temperature is from about 297 K up to above 40000 K. The wide region experimental data are used to evaluate the available theoretical models. It is found that, for neon below 1.1g/cm³ and for krypton below 2 g/cm³, within the framework of density functional theory molecular dynamics, a van der Waals correction is meaningful. Under high pressure and temperature, results from the self-consistent fluid variational theory model are sensitive to the potential parameter and could give successful predictions in the whole experimental regime if a set of proper parameters is employed. The new observations on neon and krypton under megabar (1 Mbar = 10¹¹ Pa) pressure and eV temperature (1 eV ≈ 10⁴ K) enrich the understanding on properties of warm dense matter and have potential applications in revealing the formation and evolution of high-energy density physics.