<p>Core–shell structures are widely found in composite electrodes, phase transforming of active particles and the formation of solid electrolyte interphase (SEI) membrane covering active particles in lithium-ion batteries. A general analytical solution of diffusion problem and mechanical deformation problem in a spherical core–shell electrode under traction-free boundary condition and potentiostatic operation is presented, using the method of variable substitution and separation of variables. By assigning different material properties to the shell, the analytical solution can degenerate into various forms. When the shell is electrochemically inactive, the solution corresponds to the core–shell model for the SEI/electrode structure. As the elastic modulus ratio of the shell to the core approaches infinity, the solution simplifies to a solid spherical electrode with a fully constrained surface, resembling carbon-shell-covered particles. If the core and shell are made of the same material, the core–shell model reduces to a solid spherical electrode with traction-free boundary conditions. Parameter analyses are conducted, and the results indicate that a thicker shell, a higher elastic modulus of the shell, and a larger partial molar volume of the shell lead to an increase in the absolute values of the stress components in the spherical core–shell electrode.</p>