Solid electrolytes (SEs) face significant technical challenges, in large part because they readily penetrate through SEs, leading to short circuits, even though, early-on, the high mechanical strength of ceramic separators was expected to suppress lithium growth. The ability of such a soft material to penetrate through a ceramic is surprising from the point of view of models widely used in the Li battery field. We introduce a concept, new to the battery field, for suppressing penetration of lithium dendrites through SEs by putting the SE surfaces into states of residual compressive stress. For a sufficiently high compressive stress, cracks have difficulty forming, and cracks that do form are forced to close.  Under these conditions, we expect that dendrite penetration will be inhibited or prevented. This approach is widely used to solve commercially important stress corrosion cracking problems in metals and static fatigue problems in ceramics and glasses (e.g., Gorilla Glass). However, the technique will not be useful for SEs if the Li ion transport rate through a SE is substantially reduced when the SE is in compression. Our molecular dynamics calculations for Li ion transport through a common SE demonstrate that the introduction of even very high residual compressive stresses (10 GPa) has only a modest effect on Li ion transport kinetics, suggesting that the approach is viable and capable of providing a new paradigm for developing high performance and mechanically strong SEs.