Abstract: For two-dimensional anisotropic body with a parabolic boundary, the simple explicit expressions of Green’s functions are presented when a concentraled force f is applied at a point (x₁⁰, x₂⁰) in material for two kind boundary conditions, which are of free surfoce and rigid surface. When parabolic curve degenerales into a half-infinite crack or a half-infinite rigid defect the stress singular fields near the crack tip are obtained by using the results obtained. Specially, when the concentrated force f is applied at a point on the parabolic boundary, its Green’s functions are studied, too. By them and its integral, the arbitrary parabolic boundary value problems can be solved. The limit case that the boundary degenerates into a crack is studied and the corresponding stress intensity factors are obtained.