Abstract: Many metal materials exhibit the properties of orthotropic hardening under loading. In this paper, the R.Hill yield criterion is used to discuss the characteristic field of plane stress problem for orthotropic materials. Dimensionless analytical solutions are obtained from the differential equations of equilibrium, and the coefficients of the characteristic curves are determined. It is found that the characteristic curves are not orthogonal generally. The stresses at press load boundary are studied and the characteristic fields of different stress state areas are obtained. Analysis of the transition area is also conducted using the numerical method.