A Green's-function method is employed to provide a rigorous analysis to the propagation and coupling phenomena in holey fibers. The analysis is carried out for an arbitrary grid of circular air holes of the fiber guide, while the electromagnetic field is taken to be a vector quantity. Application of the Green's-function concept leads to a coupled system of equations incorporating as unknowns the field expansion coefficients to cylindrical wave functions within the air holes. The propagation constants of the guided waves are computed accurately by determining the singular points of the corresponding system's matrix. Field distribution and dispersion properties of guided modes as well as coupling phenomena between parallel-running holey fibers are investigated, and numerical results are presented.