In this paper, we propose a rigorous frequency domain surface integral formulation to efficiently model arbitrarily shaped conductors. It includes the skin effect via the lossy Green's function. It can also be extended to the low frequency regime to ensure the necessary wide-band coverage. In the high frequency limit, as skin depth approaches zero, our formulation resembles the impedance boundary condition (IBC), which is why it is named generalized impedance boundary condition (GIBC).