We have employed Hill's 1948 yield criterion to predict the forming limit curve for planar anisotropic sheet materials by using bifurcation theory. The effects of the material anisotropic parameters, R0, R45 and R90, on the orientation of the neck and the forming limit diagram are analyzed in a systematic manner. It is found that in biaxial stretching, the value of R0 significantly affects the limit strains, whereas R90 has a small contribution. On the other hand, R45 has no effect on the limit strains. In a drawing mode of deformation, the effects of the R's on the limit strains are insignificant. The calculated shear band (or localized neck) is assumed to take place along the zero-extension direction independently of the R values. In the case of biaxial tension deformation, the neck will always form along a principal direction. For a sheet material whose anisotropic parameter R in the major strain direction is smaller than that in the minor strain direction, the neck will form along the major strain if the state of deformation is in the vicinity of equal-biaxial stretching. In all other cases the neck will form along the minor strain direction. The forming limits as predicted by this model agree well with experimental data.