Analytic expressions are derived for the long-range falloff of the force constants of nearly-free-electron metals. Comparison with exact results shows that Friedel oscillations dominate the force constants of fcc Al beyond the fourth-neighbor shell. Applications suggested include improving embedding theories of defect-related strain, improving methods for determining force constants empirically, and realistically assessing Friedel oscillation contributions to interadsorbate and interstep interactions at surfaces. {copyright} {ital 1997} {ital The American Physical Society}