In this paper, we establish the exponential convergence theory for the multipole and local expansions, shifting and translation operators for the Green’s function of 3-dimensional Laplace equation in layered media. An immediate application of the theory is to ensure the exponential convergence of the FMM which has been shown by the numerical results reported in [27]. As the Green’s function in layered media consists of free space and reaction field components and the theory for the free space components is well known, this paper will focus on the analysis for the reaction components. We first prove that the density functions in the integral representations of the reaction components are analytic and bounded in the right half complex wave number plane. Then, by using the Cagniard-de Hoop transform and contour deformations, estimates for the remainder terms of the truncated expansions are given, and, as a result, the exponential convergence for the expansions and translation operators is proven.