Abstract: A numerical method is presented for lower bound limit and shakedown analyses of orthotropic structures.The Hill's yield criterion is introduced into the static limit and shakedown theorem and using temperature parameter method is used to construct self-stress field.The finite element modeling is deduced into a nonlinear mathematical programming with inequality-constraint conditions,which can be solved by the Sequential Quadratic Programming method(SQP).Some examples are illustrated to show the application of the present approach.