Abstract: The relation expression of Drucker-Prager(D-P)yield criterions matched Mohr-Coulomb(M-C)yield criterion were obtained based on the Lode angle parameter.The transformation method of different Drucker-Prager yield criterion was put forward.The Drucker-Prager yield criterions matched Mohr-Coulomb yield criterion were studied profoundly.Finally,a foundation under plane strain condition was analyzed by FEM through the Drucker-Prager yield criterions.A lot of valuable results were got by contrast to the solutions of Prandtl theory and the theory of Drucker-Prager yield criterions matched Mohr-Coulomb yield criterion was proved to be correct which could be applied to the analysis of practical geotechnical engineering.