Abstract: The expressions for pijkl of the elastoplastic incremental constitutive equation （Eq. 6） are derived in non-orthogonal curvilinear coordinates （Eqs. 15 and 19）. Choice of a proper curvilinear coordinate system sometimes makes the problem easy to treat, especially the boundary conditions to be satisfied easily and exactly. - From these general equations the eiastoplastic matrix for finite element method can be obtained in any specific coordinate system.The adaptability and flexibility of conventional finite difference method are greatly enhanced by using non-orthogonal curvilinear coordinates. The eiastoplastic constitutive equation expressed in curvilinear coordinates also provides explicit stiffness coefficients for solving elastoplas?tic problems with curvilinear finite difference.