A relaxation condition of the strain space formulation and a relaxatio
n theory of plasticity for anisotropic metallic materials, which may b
e undertaken in parallel with Hill's stress-based yield criterion and
the traditional plasticity theory as an alternative approach, are deve
loped. The calculated relaxation loci corresponding to different effec
tive stress relaxation for zirconium alloys demonstrate certain advant
ages in description of mechanical behaviour of elastic-plastic anisotr
opic metallic materials.