Core-shell composite structures are potential candidates for Li-ion battery electrodes as they can take advantage of materials with higher energy density and materials with higher cyclability. This paper derives an analytical solution for isotropic 1-dimensional diffusion with galvanostatic boundary condition in composite slab, cylinder and sphere using separation of variables method. A general interfacial condition has been used to represent the dynamics at the interface of the composite material rendering the solution useful for wide variety of battery materials. Using the derived analytical solution for diffusion, intercalation induced stresses were estimated for spherical core-shell materials. (C) 2014 The Electrochemical Society. All rights reserved.