In a novel design of lithium-ion batteries, hollow electrode particles coated with stiff shells are used to mitigate mechanical and chemical degradation. In particular, silicon anodes of such core shell nanostructures have been cycled thousands of times with little capacity fading. To reduce weight and to facilitate lithium diffusion, the shell should be thin. However, to avert fracture and debonding from the core, the shell must be sufficiently thick. This tradeoff is considered here by calculating the stress fields resulting from concurrent insertion reaction and plastic flow for both spherical and cylindrical hollow core-shell nanostructures. Conditions to avert fracture and debonding are identified in terms of the radius of the core, the thickness of the shell, and the state of charge. The effect of the stress on the electrochemical reaction is also discussed. (C) 2012 Elsevier B.V. All rights reserved.