The calculation procedure of the continuum mechanics of textured polycrystals (CMTP) method is reviewed to estimate calculating time with various yield functions (YFs). A so called semi quadratic YF is proposed to eliminate time consuming numerical calculation and avoid the decrease of prediction precision. The reasonability of the new YF is proved by making the comparisons between predicted R values and earing behaviour for some materials and the experimental results. The calculation procedure of the continuum mechanics of textured polycrystals (CMTP) method is reviewed to estimate calculating time with various yield functions (YFs). A so called semi quadratic YF is proposed to eliminate time consuming consuming numerical calculation and avoid the decrease of prediction precision. The reasonability of the new YF is proved by making the comparisons between predicted R values ​​and earing behavior for some materials and the experimental results.