ABSTRACT The Matsuoka-Nakai failure criterion for a frictional material, and the Von Mises criterion for a cohesive material are expressed in such a way that they are seen to bear similar relationships to the cohesionless Mohr-Coulomb and Tresca criteria respectively. A generalisation of the Matsuoka-Nakai and Von Mises criteria for materials with friction and cohesion is described, which bears a similar relationship to the general Mohr-Coulomb criterion. The new criterion is expressed conveniently in terms of principal stresses, and is also expressed in terms of stress invariants.