  Integral expressions are determined for the elastic displacement and stress
fields due to stationary or moving dislocation loops in finite samples. These
general expressions are valid for anisotropic media as well. Specifically for
the stress fields, a line integral representation is found, thus showing
rigorously the independence of the stress fields with respect to the choice of
slip planes. In the stationary case the line integral representation involves
calculating a "vector potential" dependent on the specific geometry of the
sample. Two examples of geometries, isotropic half space and thin plate, are
shown where the "vector potential" has been explicitly determined. With this
general method one recovers some earlier specific results in these geometries.
