Metallic lithium and sodium are actively investigated as anodes for all solid-state batteries. While the mechanical properties of Li and Na remain poorly understood, there is a growing consensus that they play a crucial role in determining the integrity of solid electrolytes. The mechanical properties of Li and Na are complicated by the rich variety of martensitic transformations that they undergo upon cooling below room temperature. Here, we develop an overarching crystallographic description that connects the high temperature bcc forms of Li and Na to the large number of close-packed phases that Li and Na transform to at low temperatures. First-principles calculations predict that Li and Na have unusually flat energy surfaces as a function of a minimal set of strain and shuffle order parameters that describe pathways between bcc and close-packed structures. Calculated generalized stacking fault energies of close-packed Li and Na phases are similarly very flat, indicating a negligible resistance to dislocation motion. The remarkably shallow energy surfaces of Li and Na as a function of strain and shuffle deformations suggest that these metals are unusually soft and should exhibit negligible resistance to plastic deformation.