A full nonlocal pseudopotential calculation of the surface tension of simple liquid metals is presented. The basis of the theory is the direct perturbation expansion to second order in a weak electron-ion pseudopotential. By invoking the Born-Oppenheimer adiabatic approximation, an effective Hamiltonian is obtained. This effective Hamiltonian is then used, in conjunction with Gibbs-Bogoliubov inequality, to derive tractable expressions for the calculation of surface tension of simple liquid metals. It is found that, within the same approximation, our nonlocal pseudopotential calculations yield surface tensions of liquid metals much smaller than similar calculations obtained by Hasegawa and Watabe [J. Phys. C 15, 353 (1982)]. However, a review of the theory and a close examination of the various contributions to the surface tension show that the results of calculations by Hasegawa and Watabe are to some extent fortuitous. Various possible improvements and sources of discrepancies on the computation of surface tension will be checked and discussed in the text.