The elastic displacement and stress fields due to a polygonal dislocation within an anisotropic homogeneous half-space are studied in this paper. Simple line integrals from 0 to π for the elastic fields are derived by applying the point-force Green’s functions in the corresponding half-space. Notably, the geometry of the polygonal dislocation is included entirely in the integrand easing integration for any arbitrarily shaped dislocation. We apply the proposed method to a hexagonal shaped dislocation loop with Burgers vector along [$1\xaf$ 1 0] lying on the crystallographic (1 1 1) slip plane within a half-space of a copper crystal. It is demonstrated numerically that the displacement jump condition on the dislocation loop surface and the traction-free condition on the surface of the half-space are both satisfied. On the free surface of the half-space, it is shown that the distributions of the hydrostatic stress (σ11 + σ22 )/2 and pseudohydrostatic displacement (u1 + u2 )/2 are both anti-symmetric, while the biaxial stress (σ11 − σ22 )/2 and pseudobiaxial displacement (u1 − u2 )/2 are both symmetric.