In this article, through summarizing experimental data of shock-wave compression for thirty-four metallic elements, we have obtained a generally applicable empirical expression for the reduced Hugoniot curve, which describes the law of shock-wave compressions for metallic elements. In treating these data, the principle of corresponding state was employed. By utilizing the obtained reduced Hugoniot curve and basing on the Debye theory, we have derived a generally applicable equation of state for metallic elements under high pressures. We used this equation of state to calculate the pressure-compression curves for fifteen metallic elements (magnesium, iron, copper, etc). The comparison shows that the calculated values are in good agreement with experimental data.