Shock melting in single crystal Al and Cu along the principle Hugoniot was investigated through molecular dynamics simulations. First, the GRAY equation of state (EOS) was employed to reproduce the melting curve, which aimed at obtaining the Simon melting equation. The accuracy and validity of Simon melting curve are evaluated by the first-order derivative of melting temperature with respect to pressure at zero pressure, initial and complete melting temperatures and pressures, which are in good agreement with the available data. Next, the specific melting volume and latent heat calculated by the Clausius-Clapeyron equation present a descending and ascending trend as pressure increases, respectively. Then it is assumed that the liquid fraction is a power law function of pressure, whose nonlinear increasing is featured by the symmetry. More importantly, the expression of second-order derivative of melting temperature with respect to pressure is deduced by the Clausius-Clapeyron relation and Simon melting equation, respectively. Specifically for the Clausius-Clapeyron relation, its application to solid-liquid phase transformation for Al and Cu is quite effective and the result of the second-order derivative at zero pressure is reasonably compatible with that calculated from the Simon melting equation, which manifests that this two methods can be verified mutually. Moreover, it further discusses that the change characteristics of Simon melting equation by virtue of its first- and second-order derivatives.