We have simulated the shock Hugoniot of copper and uranium based on the results of first principles electronic structure calculations. The room temperature isotherm has been obtained by evaluating the accurate ground state total energies at various compressions, and the thermal and electronic excitation contributions were obtained by adopting isotropic models using the results obtained by the band structure calculations. Our calculations ensure smooth consideration of pressure ionization effects as the relevant core states are treated in the semi-core form at the ambient pressure. The pressure variation of the electronic Grüneisen parameter was estimated for copper using the band structure results, which leads to good agreement of the simulated shock Hugoniot with the measured shock data. The simulation results obtained for U are also compared with the experimental data available in literature and with our own data.