The mathematical expressions of internal friction angle considering the influence of intermediate principal stress under true triaxial stress were deduced. After a comparison of the results of the true triaxial tests of gravel, Q2 loess and Santa Monica Beach sand, the relationships between internal friction angle and intermediate principal stress coefficient were studied based on DP yield criteria. The results show that the calculated values of internal friction angle with D-P yield criteria equal the testing results when the intermediate principal stress coefficient is suitable for the corresponding criterion. In order to obtain reasonable results, appropriate D-P yield criteria should be chosen for different materials.