Abstract: A slip-line field theory of transversely isotropic body is proposed in the presentpaper in order to deal with problems in geology and geotechniques.The Goldenblat-Kopnov failure criterion is employed.The parameters in it are treated as functions of tempperature It is applicable to transverse isotropic media in non-uniform temperaturefield.The basic equtions of plastic deformation are developed while the associated ru-les of flow are derived.By means of characteristic line theory,slip-line slope formulasand laws of variation of stress and velocity along slip lines are obtained,The indenta-tion on semi-infinite media is calculated.The theory developed in this paper may be simplified into many classical theories such as Mises,Hill,and Coulomb ones,This complicated theory may be applied to geotechniques,geological structures,petroleumindustry,mining engineering,etc.

Key words: simply supported beam, functionally gradient materials (FGM), analytical solution, piezoelectric material, slip-line field, transversely isotropic, non-uniform temperaturefield, failure criterion, limit equilibrium