A theory is presented for the determination of three coefficients characterizing anisotropic materials. These new coefficients of anisotropy advantageously replace Lankford’s classic empirical coefficient, r, in the definition of the anisotropy of a rolled sheet. It is shown how these coefficients rho(0), rho(45) and rho(90), may be deduced from the theory, provided certain assumptions are made concerning the rolled material. The validity of the theory was tested through experiments on rolled ultra high-purity iron sheet, rho(0), rho(45) and rho(90), being determined by means of a special purpose-built extensometer.