Hypersonic high-enthalpy laminar flows over a 25-55° double-cone and a hollow cylinder with a 30° flare geometries are simulated using the US3D unstructured flow solver developed at the University of Minnesota. The geometries considered were used in earlier CFD code validation studies at low enthalpy conditions which had favorable comparisons with simulation data. The present high-enthalpy flow conditions were taken from the experimental database assembled from experiments performed at the LENS-XX high-enthalpy expansion tunnel facility at CUBRC with air as the test gas. Free-stream total enthalpy in the experiments ranges from 10.4 to 21.9 MJ/kg and Reynolds number varies from 110,000 to 420,000 per meter. The resulting axisymmetric flow-fields are expected to remain laminar. Numerical predictions employ standard physical models for flowfield chemistry and internal energy relaxation. Simulations predict steady flowfields that evolve very slowly to steady state. Grid convergence is demonstrated and grids of up to 2048×l1024 points used. Different models of internal energy are also used in these simulations. Surface heat-flux results are presented for a cold wall with and without catalytic effects.