A method is described for determining the elastic constants of a crystalline material from measurements of the first two longitudinal frequencies of long bars of rectangular cross section. The method is based upon the relationships between the elastic constants and both Young's modulus and the dispersion of longitudinal waves. The expression for the dispersion, derived with the aid of perturbation theory, is applicable to specimens of the most general (triclinic) anisotropy. The method yields the following values for the elastic compliances of silicon (in cm2/dyn × 1013):S11 = 7.704±0.4%,S12 = −2.234±2.8%,S44 = 12.692±2.5%. A self‐consistency check yieldsS12 = −2.254±11.5%. These values are compared to those of other workers using high‐frequency methods.