Abstract: By the nonlocal continuum theory,with small strain and small local rotationassumption,we consider the effect of body couple for asymmetric stress field by assumingthat the energy functions of symmetric and the asymmetric part of stress can be formulatedindep endent ly By means of t he principle of thermo dynamics and the concept of yieldsurface,a new t heory for nonfo cal asymmet ric elasto- plasticity is est ablished