Abstract: On condition that any perfectly plastic stress component near a singular point is nothing but the function of θ only, making use of equilibrium equations and Hill anisotropic yield condition, we derive the general analytical expressions of the anisotropic plastic stress field near a singular point in both the cases of anti-plane and in-plane strains. Applying these general analytical expressions to the concrete cracks and the plane-strain bodies with a singular point, the anisotropic plastic stress fields at the tips of Mode Ⅰ, Mode Ⅱ, Mode Ⅲ and mixed mode Ⅰ-Ⅱ cracks, and the limit loads of anisotropic plastic plane-strain bodies with a singular point are obtained.