Abstract: This paper addresses the linear Mohr-Coulomb yield criterion and Drucker-Prager yield criterion, and the relation among the linear Mohr-Coulomb criteria in material mechanics and rock mechanics. The geometrical characteristics of the linear Mohr-Coulomb yield surface and the Drucker-Prager yield surface are described. The linear Mohr-Coulomb criterion is approximated using the Drucker-Prager criterion in three ways and the resultant differences are highlighted. An example is given in which the Drucker-Prager criterion is used to fit the linear Mohr-Coulomb criterion.