A new Drucker yield function for an orthorhombic aggregate of cubic crystallites is proposed. The related function κ(η) between the Drucker yield function and the Hershey yield function is determined. The Drucker yield function and the Hershey yield function with the related function κ(η) have good consistency. We get the yield stresses and the q-values of isotropic polycrystals from the Drucker yield function and the Hershey yield function under the biaxial tensional stretching. In the case of anisotropy, the uniaxial yield stress and q-value with effects of the texture coefficients and {the directional dependence} are derived from the new Drucker yield function. The parameters Yiso,κ ) can be determined by{ fitting the data of the Taylor--Bishop--Hill theory }under the biaxial tensional stretching. The material parameters (β,γ) are obtained by fitting the yield stress and the q-value of the Taylor--Bishop--Hill theory }under the uniaxial tensional stretching. The new Drucker yield function for the orthorhombic aggregate of cubic crystallites can precisely reproduce the predictions of the Taylor--Bishop--Hill theory. The plastic yield stress Yθ and the q-value qθ based on the new Drucker yield function under the uniaxial tensional stretching can fit the experimental data Yi, qi) of steel sheets and aluminium sheets very well. The material parameters (Yiso, βc4m0,γc4m0) of the new Drucker yield function are determined via the experimental data.