In lithium-ion batteries, electrochemical driving forces promote mass transport and stimulate chemical interactions. These processes generate stresses that can cause fracture of the electrodes, thereby diminishing their capacity. Fortunately, plastic deformation and geometric design can reduce the driving force for fracture. In this talk, I will focus on these issues in silicon, germanium, and lithium metal anodes, which have enormous theoretical storage capacities but have achieved little success in practice. In particular, I will discuss experimental techniques to measure mechanical properties (elastic modulus, flow stresses, and fracture toughness) in high-capacity anodes as a function of concentration of lithium. Our theories and experiments reveal the essential conditions required to mitigate mechanical damage in these systems and thus pave the way toward realizing new high-capacity anodes.