The maximum work principle of Bishop-Hill was developed to analyze the axisymmetric co-deformation in face-centered cubic crystals (f.c.c.) for twinning on {111} 112 and slip on {111} 110 systems. The influence of ξ , the ratio of critical re- solved shear stress for twinning to slip, on the yield stress states and corresponding active slip or/and twinning systems for orientations in the standard stereographic triangle of cubic crystal was investigated systematically. The Taylor factors and the anisotropy of yield strength for three important orientations [100], [110] and [111] in orientation space were analyzed. It is found that the yield strength asymmetry for the case of axisymmetric de- formation of tension and compression can be explained based on the microscopic theory of crystal plasticity. The concept of orientation factor for twinning ability was proposed and the deformation mechanism map in the orientation space was established for the case of axisymmetric deformation. The deformation texture formation and development of f.c.c. crystals with low stacking fault energy for axisymmetric tension can be explained qualita- tively on the basis of analyzed results. The maximum work principle of Bishop-Hill was developed to analyze the axisymmetric co-deformation in face-centered cubic crystals (fcc) for twinning on {111} 112 and slip on {111} 110 systems. The influence of ξ, the ratio of critical re- solved shear stress for twinning to slip, on the yield stress states and corresponding active slip or / and twinning systems for orientations in the standard stereographic triangle of cubic crystal was investigated systematically. The Taylor factors and the anisotropy of yield strength for three important orientations [100], [110] and [111] in orientation space were analyzed. It is found that the yield strength asymmetry for the case of axisymmetric de- formation of tension and compression can be based on the microscopic theory of crystal plasticity . The concept of orientation factor for twinning ability was proposed and the deformation mechanism map in the orientation space was established for the case of axisymmetric deformation. The d eformation texture formation and development of f.c.c. crystals with low stacking fault energy for axisymmetric tension can be explained qualita- tively on the basis of analyzed results.